1.12: Difference between revisions

Latest revision as of 11:00, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
1.12#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}} `A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	A[k] = b[k]A[k - 1]+ a[k]A[k - 2]	Subscript[A, k] == Subscript[b, k]Subscript[A, k - 1]+ Subscript[a, k]Subscript[A, k - 2]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}} `B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	B[k] = b[k]B[k - 1]+ a[k]B[k - 2]	Subscript[B, k] == Subscript[b, k]Subscript[B, k - 1]+ Subscript[a, k]Subscript[B, k - 2]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1} = 1} `A_{-1} = 1`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	A[- 1] = 1	Subscript[A, - 1] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0} = b_{0}} `A_{0} = b_{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	A[0] = b[0]	Subscript[A, 0] == Subscript[b, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{-1} = 0} `B_{-1} = 0`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	B[- 1] = 0	Subscript[B, - 1] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0} = 1} `B_{0} = 1`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	B[0] = 1	Subscript[B, 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}} `A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	A[n]B[n - 1]- B[n]A[n - 1] = (- 1)^(n - 1)* product(a[k], k = 1..n)	Subscript[A, n]Subscript[B, n - 1]- Subscript[B, n]Subscript[A, n - 1] == (- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}} `C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	C[n]- C[n - 1] = ((- 1)^(n - 1)* product(a[k], k = 1..n))/(B[n - 1]*B[n])	Subscript[C, n]- Subscript[C, n - 1] == Divide[(- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None],Subscript[B, n - 1]*Subscript[B, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}} `a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[n] = (A[n - 1]B[n]- A[n]B[n - 1])/(A[n - 1]B[n - 2]- A[n - 2]B[n - 1])	Subscript[a, n] == Divide[Subscript[A, n - 1]Subscript[B, n]- Subscript[A, n]Subscript[B, n - 1],Subscript[A, n - 1]Subscript[B, n - 2]- Subscript[A, n - 2]Subscript[B, n - 1]]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}} `a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[n] = (B[n])/(B[n - 2])*(C[n - 1]- C[n])/(C[n - 1]- C[n - 2])	Subscript[a, n] == Divide[Subscript[B, n],Subscript[B, n - 2]]*Divide[Subscript[C, n - 1]- Subscript[C, n],Subscript[C, n - 1]- Subscript[C, n - 2]]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}} `b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[n] = (A[n]B[n - 2]- A[n - 2]B[n])/(A[n - 1]B[n - 2]- A[n - 2]B[n - 1])	Subscript[b, n] == Divide[Subscript[A, n]Subscript[B, n - 2]- Subscript[A, n - 2]Subscript[B, n],Subscript[A, n - 1]Subscript[B, n - 2]- Subscript[A, n - 2]Subscript[B, n - 1]]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}} `b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[n] = (B[n])/(B[n - 1])*(C[n]- C[n - 2])/(C[n - 1]- C[n - 2])	Subscript[b, n] == Divide[Subscript[B, n],Subscript[B, n - 1]]*Divide[Subscript[C, n]- Subscript[C, n - 2],Subscript[C, n - 1]- Subscript[C, n - 2]]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = A_{0}} `b_{0} = A_{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[0] = A[0]	Subscript[b, 0] == Subscript[A, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = B_{1}} `b_{1} = B_{1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[1] = B[1]	Subscript[b, 1] == Subscript[B, 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = A_{1}-A_{0}B_{1}} `a_{1} = A_{1}-A_{0}B_{1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[1] = A[1]- A[0]*B[1]	Subscript[a, 1] == Subscript[A, 1]- Subscript[A, 0]*Subscript[B, 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}} `C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	C[n](w) = (A[n]+ A[n - 1]w)/(B[n]+ B[n - 1]w)	Subscript[C, n][w] == Divide[Subscript[A, n]+ Subscript[A, n - 1]w,Subscript[B, n]+ Subscript[B, n - 1]w]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{0}\not = \infty} `C_{0}\not = \infty`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	C[0] <> infinity	Subscript[C, 0] \[NotEqual]*Infinity	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12#Ex14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{n}\not = C_{n-1}} `C_{n}\not = C_{n-1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	C[n] <> C[n - 1]	Subscript[C, n] \[NotEqual]*Subscript[C, n - 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|b_{n}\| \geq \|a_{n}\|+1} `\|b_{n}\| \geq \|a_{n}\|+1`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	abs(b[n]) >= abs(a[n])+ 1	Abs[Subscript[b, n]] >= Abs[Subscript[a, n]]+ 1	Skipped - no semantic math	Skipped - no semantic math	-	-
1.12.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}} `-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	-(1)/(2)*Pi + delta < argument(b[n])	-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[b, n]]	Failure	Failure	Failed [27 / 300] Result: -.70796327e-1 < -1.047197551 Test Values: {delta = 1.5, b[n] = 1/2-1/2I3^(1/2), n = 1, n = 3} Result: -.70796327e-1 < -1.047197551 Test Values: {delta = 1.5, b[n] = 1/2-1/2I3^(1/2), n = 2, n = 3} Result: -.70796327e-1 < -1.047197551 Test Values: {delta = 1.5, b[n] = 1/2-1/2I3^(1/2), n = 3, n = 3} Result: -.70796327e-1 < -2.617993878 Test Values: {delta = 1.5, b[n] = -1/23^(1/2)-1/2I, n = 1, n = 3} ... skip entries to safe data	Failed [49 / 100] Result: Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
1.12.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta} `\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	argument(b[n]) < (1)/(2)*Pi - delta	Arg[Subscript[b, n]] < Divide[1,2]*Pi - \[Delta]	Failure	Failure	Failed [72 / 300] Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, b[n] = -1.5, n = 1, n = 3} Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, b[n] = -1.5, n = 2, n = 3} Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, b[n] = -1.5, n = 3, n = 3} Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, b[n] = -.5, n = 1, n = 3} ... skip entries to safe data	Failed [64 / 100] Result: Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
1.12.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}} `-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	-(1)/(2)*Pi + delta < argument(C[n])	-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[C, n]]	Failure	Failure	Failed [27 / 300] Result: -.70796327e-1 < -1.047197551 Test Values: {delta = 1.5, C[n] = 1/2-1/2I3^(1/2), n = 1, n = 3} Result: -.70796327e-1 < -1.047197551 Test Values: {delta = 1.5, C[n] = 1/2-1/2I3^(1/2), n = 2, n = 3} Result: -.70796327e-1 < -1.047197551 Test Values: {delta = 1.5, C[n] = 1/2-1/2I3^(1/2), n = 3, n = 3} Result: -.70796327e-1 < -2.617993878 Test Values: {delta = 1.5, C[n] = -1/23^(1/2)-1/2I, n = 1, n = 3} ... skip entries to safe data	Failed [49 / 100] Result: Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
1.12.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta} `\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	argument(C[n]) < (1)/(2)*Pi - delta	Arg[Subscript[C, n]] < Divide[1,2]*Pi - \[Delta]	Failure	Failure	Failed [72 / 300] Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, C[n] = -1.5, n = 1, n = 3} Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, C[n] = -1.5, n = 2, n = 3} Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, C[n] = -1.5, n = 3, n = 3} Result: 3.141592654 < 3.070796327 Test Values: {delta = -1.5, C[n] = -.5, n = 1, n = 3} ... skip entries to safe data	Failed [64 / 100] Result: Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
1.12.E28	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}\|b_{n}\| = \infty} `\sum^{\infty}_{n=1}\|b_{n}\| = \infty`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	sum(abs(b[n]), n = 1..infinity) = infinity	Sum[Abs[Subscript[b, n]], {n, 1, Infinity}, GenerateConditions->None] == Infinity	Skipped - no semantic math	Skipped - no semantic math	-	-

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex1 1.12#Ex1] || [[Item:Q428|<math>A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[k] = b[k]*A[k - 1]+ a[k]*A[k - 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, k] == Subscript[b, k]*Subscript[A, k - 1]+ Subscript[a, k]*Subscript[A, k - 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex1 1.12#Ex1] || <math qid="Q428">A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[k] = b[k]*A[k - 1]+ a[k]*A[k - 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, k] == Subscript[b, k]*Subscript[A, k - 1]+ Subscript[a, k]*Subscript[A, k - 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex2 1.12#Ex2] || [[Item:Q430|<math>B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[k] = b[k]*B[k - 1]+ a[k]*B[k - 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, k] == Subscript[b, k]*Subscript[B, k - 1]+ Subscript[a, k]*Subscript[B, k - 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex2 1.12#Ex2] || <math qid="Q430">B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[k] = b[k]*B[k - 1]+ a[k]*B[k - 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, k] == Subscript[b, k]*Subscript[B, k - 1]+ Subscript[a, k]*Subscript[B, k - 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex3 1.12#Ex3] || [[Item:Q431|<math>A_{-1} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[- 1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, - 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex3 1.12#Ex3] || <math qid="Q431">A_{-1} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{-1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[- 1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, - 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex4 1.12#Ex4] || [[Item:Q432|<math>A_{0} = b_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0} = b_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[0] = b[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 0] == Subscript[b, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex4 1.12#Ex4] || <math qid="Q432">A_{0} = b_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{0} = b_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[0] = b[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 0] == Subscript[b, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex5 1.12#Ex5] || [[Item:Q433|<math>B_{-1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[- 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, - 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex5 1.12#Ex5] || <math qid="Q433">B_{-1} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[- 1] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, - 1] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex6 1.12#Ex6] || [[Item:Q434|<math>B_{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex6 1.12#Ex6] || <math qid="Q434">B_{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E7 1.12.E7] || [[Item:Q435|<math>A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[n]*B[n - 1]- B[n]*A[n - 1] = (- 1)^(n - 1)* product(a[k], k = 1..n)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, n]*Subscript[B, n - 1]- Subscript[B, n]*Subscript[A, n - 1] == (- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E7 1.12.E7] || <math qid="Q435">A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[n]*B[n - 1]- B[n]*A[n - 1] = (- 1)^(n - 1)* product(a[k], k = 1..n)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, n]*Subscript[B, n - 1]- Subscript[B, n]*Subscript[A, n - 1] == (- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E8 1.12.E8] || [[Item:Q436|<math>C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n]- C[n - 1] = ((- 1)^(n - 1)* product(a[k], k = 1..n))/(B[n - 1]*B[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n]- Subscript[C, n - 1] == Divide[(- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None],Subscript[B, n - 1]*Subscript[B, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E8 1.12.E8] || <math qid="Q436">C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n]- C[n - 1] = ((- 1)^(n - 1)* product(a[k], k = 1..n))/(B[n - 1]*B[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n]- Subscript[C, n - 1] == Divide[(- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None],Subscript[B, n - 1]*Subscript[B, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E10 1.12.E10] || [[Item:Q438|<math>a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = (A[n - 1]*B[n]- A[n]*B[n - 1])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == Divide[Subscript[A, n - 1]*Subscript[B, n]- Subscript[A, n]*Subscript[B, n - 1],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E10 1.12.E10] || <math qid="Q438">a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = (A[n - 1]*B[n]- A[n]*B[n - 1])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == Divide[Subscript[A, n - 1]*Subscript[B, n]- Subscript[A, n]*Subscript[B, n - 1],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E11 1.12.E11] || [[Item:Q439|<math>a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = (B[n])/(B[n - 2])*(C[n - 1]- C[n])/(C[n - 1]- C[n - 2])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == Divide[Subscript[B, n],Subscript[B, n - 2]]*Divide[Subscript[C, n - 1]- Subscript[C, n],Subscript[C, n - 1]- Subscript[C, n - 2]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E11 1.12.E11] || <math qid="Q439">a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = (B[n])/(B[n - 2])*(C[n - 1]- C[n])/(C[n - 1]- C[n - 2])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == Divide[Subscript[B, n],Subscript[B, n - 2]]*Divide[Subscript[C, n - 1]- Subscript[C, n],Subscript[C, n - 1]- Subscript[C, n - 2]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E12 1.12.E12] || [[Item:Q440|<math>b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = (A[n]*B[n - 2]- A[n - 2]*B[n])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == Divide[Subscript[A, n]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E12 1.12.E12] || <math qid="Q440">b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = (A[n]*B[n - 2]- A[n - 2]*B[n])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == Divide[Subscript[A, n]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E13 1.12.E13] || [[Item:Q441|<math>b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = (B[n])/(B[n - 1])*(C[n]- C[n - 2])/(C[n - 1]- C[n - 2])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == Divide[Subscript[B, n],Subscript[B, n - 1]]*Divide[Subscript[C, n]- Subscript[C, n - 2],Subscript[C, n - 1]- Subscript[C, n - 2]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E13 1.12.E13] || <math qid="Q441">b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = (B[n])/(B[n - 1])*(C[n]- C[n - 2])/(C[n - 1]- C[n - 2])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == Divide[Subscript[B, n],Subscript[B, n - 1]]*Divide[Subscript[C, n]- Subscript[C, n - 2],Subscript[C, n - 1]- Subscript[C, n - 2]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex7 1.12#Ex7] || [[Item:Q442|<math>b_{0} = A_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{0} = A_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[0] = A[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 0] == Subscript[A, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex7 1.12#Ex7] || <math qid="Q442">b_{0} = A_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{0} = A_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[0] = A[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 0] == Subscript[A, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex8 1.12#Ex8] || [[Item:Q443|<math>b_{1} = B_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1} = B_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1] = B[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1] == Subscript[B, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex8 1.12#Ex8] || <math qid="Q443">b_{1} = B_{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1} = B_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1] = B[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1] == Subscript[B, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex9 1.12#Ex9] || [[Item:Q444|<math>a_{1} = A_{1}-A_{0}B_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = A_{1}-A_{0}B_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = A[1]- A[0]*B[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == Subscript[A, 1]- Subscript[A, 0]*Subscript[B, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex9 1.12#Ex9] || <math qid="Q444">a_{1} = A_{1}-A_{0}B_{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = A_{1}-A_{0}B_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = A[1]- A[0]*B[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == Subscript[A, 1]- Subscript[A, 0]*Subscript[B, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex10 1.12#Ex10] || [[Item:Q451|<math>C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n](w) = (A[n]+ A[n - 1]*w)/(B[n]+ B[n - 1]*w)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n][w] == Divide[Subscript[A, n]+ Subscript[A, n - 1]*w,Subscript[B, n]+ Subscript[B, n - 1]*w]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex10 1.12#Ex10] || <math qid="Q451">C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n](w) = (A[n]+ A[n - 1]*w)/(B[n]+ B[n - 1]*w)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n][w] == Divide[Subscript[A, n]+ Subscript[A, n - 1]*w,Subscript[B, n]+ Subscript[B, n - 1]*w]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex13 1.12#Ex13] || [[Item:Q454|<math>C_{0}\not = \infty</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{0}\not = \infty</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[0] <> infinity</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 0] \[NotEqual]*Infinity</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex13 1.12#Ex13] || <math qid="Q454">C_{0}\not = \infty</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{0}\not = \infty</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[0] <> infinity</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 0] \[NotEqual]*Infinity</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12#Ex14 1.12#Ex14] || [[Item:Q455|<math>C_{n}\not = C_{n-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n}\not = C_{n-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n] <> C[n - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n] \[NotEqual]*Subscript[C, n - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12#Ex14 1.12#Ex14] || <math qid="Q455">C_{n}\not = C_{n-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{n}\not = C_{n-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[n] <> C[n - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, n] \[NotEqual]*Subscript[C, n - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E25 1.12.E25] || [[Item:Q458|<math>|b_{n}| \geq |a_{n}|+1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>|b_{n}| \geq |a_{n}|+1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">abs(b[n]) >= abs(a[n])+ 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Abs[Subscript[b, n]] >= Abs[Subscript[a, n]]+ 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E25 1.12.E25] || <math qid="Q458">|b_{n}| \geq |a_{n}|+1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>|b_{n}| \geq |a_{n}|+1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">abs(b[n]) >= abs(a[n])+ 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Abs[Subscript[b, n]] >= Abs[Subscript[a, n]]+ 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/1.12.E26 1.12.E26] || [[Item:Q459|<math>-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-(1)/(2)*Pi + delta < argument(b[n])</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[b, n]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
+| [https://dlmf.nist.gov/1.12.E26 1.12.E26] || <math qid="Q459">-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-(1)/(2)*Pi + delta < argument(b[n])</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[b, n]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
 Test Values: {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
 Test Values: {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
@@ Line 60: / Line 60: @@
 Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/1.12.E26 1.12.E26] || [[Item:Q459|<math>\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>argument(b[n]) < (1)/(2)*Pi - delta</syntaxhighlight> || <syntaxhighlight lang=mathematica>Arg[Subscript[b, n]] < Divide[1,2]*Pi - \[Delta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
+| [https://dlmf.nist.gov/1.12.E26 1.12.E26] || <math qid="Q459">\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>argument(b[n]) < (1)/(2)*Pi - delta</syntaxhighlight> || <syntaxhighlight lang=mathematica>Arg[Subscript[b, n]] < Divide[1,2]*Pi - \[Delta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
 Test Values: {delta = -1.5, b[n] = -1.5, n = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
 Test Values: {delta = -1.5, b[n] = -1.5, n = 2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
@@ Line 68: / Line 68: @@
 Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/1.12.E27 1.12.E27] || [[Item:Q460|<math>-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-(1)/(2)*Pi + delta < argument(C[n])</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[C, n]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
+| [https://dlmf.nist.gov/1.12.E27 1.12.E27] || <math qid="Q460">-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-(1)/(2)*Pi + delta < argument(C[n])</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[C, n]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
 Test Values: {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
 Test Values: {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.70796327e-1 < -1.047197551
@@ Line 76: / Line 76: @@
 Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/1.12.E27 1.12.E27] || [[Item:Q460|<math>\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>argument(C[n]) < (1)/(2)*Pi - delta</syntaxhighlight> || <syntaxhighlight lang=mathematica>Arg[Subscript[C, n]] < Divide[1,2]*Pi - \[Delta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
+| [https://dlmf.nist.gov/1.12.E27 1.12.E27] || <math qid="Q460">\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>argument(C[n]) < (1)/(2)*Pi - delta</syntaxhighlight> || <syntaxhighlight lang=mathematica>Arg[Subscript[C, n]] < Divide[1,2]*Pi - \[Delta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
 Test Values: {delta = -1.5, C[n] = -1.5, n = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
 Test Values: {delta = -1.5, C[n] = -1.5, n = 2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.070796327
@@ Line 84: / Line 84: @@
 Test Values: {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/1.12.E28 1.12.E28] || [[Item:Q461|<math>\sum^{\infty}_{n=1}|b_{n}| = \infty</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum^{\infty}_{n=1}|b_{n}| = \infty</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(abs(b[n]), n = 1..infinity) = infinity</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Abs[Subscript[b, n]], {n, 1, Infinity}, GenerateConditions->None] == Infinity</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/1.12.E28 1.12.E28] || <math qid="Q461">\sum^{\infty}_{n=1}|b_{n}| = \infty</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum^{\infty}_{n=1}|b_{n}| = \infty</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(abs(b[n]), n = 1..infinity) = infinity</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Abs[Subscript[b, n]], {n, 1, Infinity}, GenerateConditions->None] == Infinity</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |}
 </div>

1.12: Difference between revisions

Latest revision as of 11:00, 28 June 2021

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