Numerical Methods - 3.3 Interpolation

From testwiki
Revision as of 11:02, 28 June 2021 by Admin (talk | contribs) (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
3.3#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n_{0} = -\tfrac{1}{2}(n-\sigma)}
n_{0} = -\tfrac{1}{2}(n-\sigma)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
n[0] = -(1)/(2)*(n - sigma)
 
Subscript[n, 0] == -Divide[1,2]*(n - \[Sigma])
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n_{1} = \tfrac{1}{2}(n+\sigma)}
n_{1} = \tfrac{1}{2}(n+\sigma)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
n[1] = (1)/(2)*(n + sigma)
 
Subscript[n, 1] == Divide[1,2]*(n + \[Sigma])
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sigma = \tfrac{1}{2}(1-(-1)^{n})}
\sigma = \tfrac{1}{2}(1-(-1)^{n})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sigma = (1)/(2)*(1 -(- 1)^(n))
 
\[Sigma] == Divide[1,2]*(1 -(- 1)^(n))
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = (1-t)f_{0}+tf_{1}+R_{1,t}}
f_{t} = (1-t)f_{0}+tf_{1}+R_{1,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < t, t < 1} 
f[t] = (1 - t)*f[0]+ t*f[1]+ R[1 , t]
 
Subscript[f, t] == (1 - t)*Subscript[f, 0]+ t*Subscript[f, 1]+ Subscript[R, 1 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1} = \tfrac{1}{8}}
c_{1} = \tfrac{1}{8}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < t, t < 1} 
c[1] = (1)/(8)
 
Subscript[c, 1] == Divide[1,8]
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-1}^{1}A_{k}^{2}f_{k}+R_{2,t}}
f_{t} = \sum_{k=-1}^{1}A_{k}^{2}f_{k}+R_{2,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{t} < 1} 
f[t] = sum((A[k])^(2)*f[k], k = - 1..1)+ R[2 , t]
 
Subscript[f, t] == Sum[(Subscript[A, k])^(2)*Subscript[f, k], {k, - 1, 1}, GenerateConditions->None]+ Subscript[R, 2 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{2} = \tfrac{1}{2}t(t-1)}
A_{-1}^{2} = \tfrac{1}{2}t(t-1)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 1])^(2) = (1)/(2)*t*(t - 1)
 
(Subscript[A, - 1])^(2) == Divide[1,2]*t*(t - 1)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{2} = 1-t^{2}}
A_{0}^{2} = 1-t^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[0])^(2) = 1 - (t)^(2)
 
(Subscript[A, 0])^(2) == 1 - (t)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{2} = \tfrac{1}{2}t(t+1)}
A_{1}^{2} = \tfrac{1}{2}t(t+1)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[1])^(2) = (1)/(2)*t*(t + 1)
 
(Subscript[A, 1])^(2) == Divide[1,2]*t*(t + 1)
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{2} = 1/(9\sqrt{3})}
c_{2} = 1/(9\sqrt{3})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{t} < 1} 
c[2] = 1/(9*sqrt(3))
 
Subscript[c, 2] == 1/(9*Sqrt[3])
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-1}^{2}A_{k}^{3}f_{k}+R_{3,t}}
f_{t} = \sum_{k=-1}^{2}A_{k}^{3}f_{k}+R_{3,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 < t, t < 2} 
f[t] = sum((A[k])^(3)*f[k], k = - 1..2)+ R[3 , t]
 
Subscript[f, t] == Sum[(Subscript[A, k])^(3)*Subscript[f, k], {k, - 1, 2}, GenerateConditions->None]+ Subscript[R, 3 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{3} = -\tfrac{1}{6}t(t-1)(t-2)}
A_{-1}^{3} = -\tfrac{1}{6}t(t-1)(t-2)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 1])^(3) = -(1)/(6)*t*(t - 1)*(t - 2)
 
(Subscript[A, - 1])^(3) == -Divide[1,6]*t*(t - 1)*(t - 2)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{3} = \tfrac{1}{2}(t^{2}-1)(t-2)}
A_{0}^{3} = \tfrac{1}{2}(t^{2}-1)(t-2)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[0])^(3) = (1)/(2)*((t)^(2)- 1)*(t - 2)
 
(Subscript[A, 0])^(3) == Divide[1,2]*((t)^(2)- 1)*(t - 2)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{3} = -\tfrac{1}{2}t(t+1)(t-2)}
A_{1}^{3} = -\tfrac{1}{2}t(t+1)(t-2)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[1])^(3) = -(1)/(2)*t*(t + 1)*(t - 2)
 
(Subscript[A, 1])^(3) == -Divide[1,2]*t*(t + 1)*(t - 2)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{3} = \tfrac{1}{6}t(t^{2}-1)}
A_{2}^{3} = \tfrac{1}{6}t(t^{2}-1)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[2])^(3) = (1)/(6)*t*((t)^(2)- 1)
 
(Subscript[A, 2])^(3) == Divide[1,6]*t*((t)^(2)- 1)
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-2}^{2}A_{k}^{4}f_{k}+R_{4,t}}
f_{t} = \sum_{k=-2}^{2}A_{k}^{4}f_{k}+R_{4,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{t} < 2} 
f[t] = sum((A[k])^(4)*f[k], k = - 2..2)+ R[4 , t]
 
Subscript[f, t] == Sum[(Subscript[A, k])^(4)*Subscript[f, k], {k, - 2, 2}, GenerateConditions->None]+ Subscript[R, 4 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t-2)}
A_{-2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t-2)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 2])^(4) = (1)/(24)*t*((t)^(2)- 1)*(t - 2)
 
(Subscript[A, - 2])^(4) == Divide[1,24]*t*((t)^(2)- 1)*(t - 2)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{4} = -\tfrac{1}{6}t(t-1)(t^{2}-4)}
A_{-1}^{4} = -\tfrac{1}{6}t(t-1)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 1])^(4) = -(1)/(6)*t*(t - 1)*((t)^(2)- 4)
 
(Subscript[A, - 1])^(4) == -Divide[1,6]*t*(t - 1)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{4} = \tfrac{1}{4}(t^{2}-1)(t^{2}-4)}
A_{0}^{4} = \tfrac{1}{4}(t^{2}-1)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[0])^(4) = (1)/(4)*((t)^(2)- 1)*((t)^(2)- 4)
 
(Subscript[A, 0])^(4) == Divide[1,4]*((t)^(2)- 1)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{4} = -\tfrac{1}{6}t(t+1)(t^{2}-4)}
A_{1}^{4} = -\tfrac{1}{6}t(t+1)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[1])^(4) = -(1)/(6)*t*(t + 1)*((t)^(2)- 4)
 
(Subscript[A, 1])^(4) == -Divide[1,6]*t*(t + 1)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t+2)}
A_{2}^{4} = \tfrac{1}{24}t(t^{2}-1)(t+2)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[2])^(4) = (1)/(24)*t*((t)^(2)- 1)*(t + 2)
 
(Subscript[A, 2])^(4) == Divide[1,24]*t*((t)^(2)- 1)*(t + 2)
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-2}^{3}A_{k}^{5}f_{k}+R_{5,t}}
f_{t} = \sum_{k=-2}^{3}A_{k}^{5}f_{k}+R_{5,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -2 < t, t < 3} 
f[t] = sum((A[k])^(5)*f[k], k = - 2..3)+ R[5 , t]
 
Subscript[f, t] == Sum[(Subscript[A, k])^(5)*Subscript[f, k], {k, - 2, 3}, GenerateConditions->None]+ Subscript[R, 5 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{5} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t-3)}
A_{-2}^{5} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t-3)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 2])^(5) = -(1)/(120)*t*((t)^(2)- 1)*(t - 2)*(t - 3)
 
(Subscript[A, - 2])^(5) == -Divide[1,120]*t*((t)^(2)- 1)*(t - 2)*(t - 3)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{5} = \tfrac{1}{24}t(t-1)(t^{2}-4)(t-3)}
A_{-1}^{5} = \tfrac{1}{24}t(t-1)(t^{2}-4)(t-3)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 1])^(5) = (1)/(24)*t*(t - 1)*((t)^(2)- 4)*(t - 3)
 
(Subscript[A, - 1])^(5) == Divide[1,24]*t*(t - 1)*((t)^(2)- 4)*(t - 3)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{5} = -\tfrac{1}{12}(t^{2}-1)(t^{2}-4)(t-3)}
A_{0}^{5} = -\tfrac{1}{12}(t^{2}-1)(t^{2}-4)(t-3)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[0])^(5) = -(1)/(12)*((t)^(2)- 1)*((t)^(2)- 4)*(t - 3)
 
(Subscript[A, 0])^(5) == -Divide[1,12]*((t)^(2)- 1)*((t)^(2)- 4)*(t - 3)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{5} = \tfrac{1}{12}t(t+1)(t^{2}-4)(t-3)}
A_{1}^{5} = \tfrac{1}{12}t(t+1)(t^{2}-4)(t-3)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[1])^(5) = (1)/(12)*t*(t + 1)*((t)^(2)- 4)*(t - 3)
 
(Subscript[A, 1])^(5) == Divide[1,12]*t*(t + 1)*((t)^(2)- 4)*(t - 3)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{5} = -\tfrac{1}{24}t(t^{2}-1)(t+2)(t-3)}
A_{2}^{5} = -\tfrac{1}{24}t(t^{2}-1)(t+2)(t-3)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[2])^(5) = -(1)/(24)*t*((t)^(2)- 1)*(t + 2)*(t - 3)
 
(Subscript[A, 2])^(5) == -Divide[1,24]*t*((t)^(2)- 1)*(t + 2)*(t - 3)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}^{5} = \tfrac{1}{120}t(t^{2}-1)(t^{2}-4)}
A_{3}^{5} = \tfrac{1}{120}t(t^{2}-1)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[3])^(5) = (1)/(120)*t*((t)^(2)- 1)*((t)^(2)- 4)
 
(Subscript[A, 3])^(5) == Divide[1,120]*t*((t)^(2)- 1)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-3}^{3}A_{k}^{6}f_{k}+R_{6,t}}
f_{t} = \sum_{k=-3}^{3}A_{k}^{6}f_{k}+R_{6,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{t} < 3} 
f[t] = sum((A[k])^(6)*f[k], k = - 3..3)+ R[6 , t]
 
Subscript[f, t] == Sum[(Subscript[A, k])^(6)*Subscript[f, k], {k, - 3, 3}, GenerateConditions->None]+ Subscript[R, 6 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t-3)(t^{2}-4)}
A_{-3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t-3)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 3])^(6) = (1)/(720)*t*((t)^(2)- 1)*(t - 3)*((t)^(2)- 4)
 
(Subscript[A, - 3])^(6) == Divide[1,720]*t*((t)^(2)- 1)*(t - 3)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t^{2}-9)}
A_{-2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t-2)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 2])^(6) = -(1)/(120)*t*((t)^(2)- 1)*(t - 2)*((t)^(2)- 9)
 
(Subscript[A, - 2])^(6) == -Divide[1,120]*t*((t)^(2)- 1)*(t - 2)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{6} = \tfrac{1}{48}t(t-1)(t^{2}-4)(t^{2}-9)}
A_{-1}^{6} = \tfrac{1}{48}t(t-1)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 1])^(6) = (1)/(48)*t*(t - 1)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, - 1])^(6) == Divide[1,48]*t*(t - 1)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{6} = -\tfrac{1}{36}(t^{2}-1)(t^{2}-4)(t^{2}-9)}
A_{0}^{6} = -\tfrac{1}{36}(t^{2}-1)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[0])^(6) = -(1)/(36)*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, 0])^(6) == -Divide[1,36]*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{6} = \tfrac{1}{48}t(t+1)(t^{2}-4)(t^{2}-9)}
A_{1}^{6} = \tfrac{1}{48}t(t+1)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[1])^(6) = (1)/(48)*t*(t + 1)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, 1])^(6) == Divide[1,48]*t*(t + 1)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t+2)(t^{2}-9)}
A_{2}^{6} = -\tfrac{1}{120}t(t^{2}-1)(t+2)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[2])^(6) = -(1)/(120)*t*((t)^(2)- 1)*(t + 2)*((t)^(2)- 9)
 
(Subscript[A, 2])^(6) == -Divide[1,120]*t*((t)^(2)- 1)*(t + 2)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t+3)(t^{2}-4)}
A_{3}^{6} = \tfrac{1}{720}t(t^{2}-1)(t+3)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[3])^(6) = (1)/(720)*t*((t)^(2)- 1)*(t + 3)*((t)^(2)- 4)
 
(Subscript[A, 3])^(6) == Divide[1,720]*t*((t)^(2)- 1)*(t + 3)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{t} = \sum_{k=-3}^{4}A_{k}^{7}f_{k}+R_{7,t}}
f_{t} = \sum_{k=-3}^{4}A_{k}^{7}f_{k}+R_{7,t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -3 < t, t < 4} 
f[t] = sum((A[k])^(7)*f[k], k = - 3..4)+ R[7 , t]
 
Subscript[f, t] == Sum[(Subscript[A, k])^(7)*Subscript[f, k], {k, - 3, 4}, GenerateConditions->None]+ Subscript[R, 7 , t]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex30 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-3}^{7} = -\tfrac{1}{5040}t(t^{2}-1)(t-3)(t-4)(t^{2}-4)}
A_{-3}^{7} = -\tfrac{1}{5040}t(t^{2}-1)(t-3)(t-4)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 3])^(7) = -(1)/(5040)*t*((t)^(2)- 1)*(t - 3)*(t - 4)*((t)^(2)- 4)
 
(Subscript[A, - 3])^(7) == -Divide[1,5040]*t*((t)^(2)- 1)*(t - 3)*(t - 4)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-2}^{7} = \tfrac{1}{720}t(t^{2}-1)(t-2)(t-4)(t^{2}-9)}
A_{-2}^{7} = \tfrac{1}{720}t(t^{2}-1)(t-2)(t-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 2])^(7) = (1)/(720)*t*((t)^(2)- 1)*(t - 2)*(t - 4)*((t)^(2)- 9)
 
(Subscript[A, - 2])^(7) == Divide[1,720]*t*((t)^(2)- 1)*(t - 2)*(t - 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{-1}^{7} = -\tfrac{1}{240}t(t-1)(t-4)(t^{2}-4)(t^{2}-9)}
A_{-1}^{7} = -\tfrac{1}{240}t(t-1)(t-4)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[- 1])^(7) = -(1)/(240)*t*(t - 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, - 1])^(7) == -Divide[1,240]*t*(t - 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}^{7} = \tfrac{1}{144}(t^{2}-1)(t-4)(t^{2}-4)(t^{2}-9)}
A_{0}^{7} = \tfrac{1}{144}(t^{2}-1)(t-4)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[0])^(7) = (1)/(144)*((t)^(2)- 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, 0])^(7) == Divide[1,144]*((t)^(2)- 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}^{7} = -\tfrac{1}{144}t(t+1)(t-4)(t^{2}-4)(t^{2}-9)}
A_{1}^{7} = -\tfrac{1}{144}t(t+1)(t-4)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[1])^(7) = -(1)/(144)*t*(t + 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, 1])^(7) == -Divide[1,144]*t*(t + 1)*(t - 4)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex35 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}^{7} = \tfrac{1}{240}t(t^{2}-1)(t+2)(t-4)(t^{2}-9)}
A_{2}^{7} = \tfrac{1}{240}t(t^{2}-1)(t+2)(t-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[2])^(7) = (1)/(240)*t*((t)^(2)- 1)*(t + 2)*(t - 4)*((t)^(2)- 9)
 
(Subscript[A, 2])^(7) == Divide[1,240]*t*((t)^(2)- 1)*(t + 2)*(t - 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}^{7} = -\tfrac{1}{720}t(t^{2}-1)(t+3)(t-4)(t^{2}-4)}
A_{3}^{7} = -\tfrac{1}{720}t(t^{2}-1)(t+3)(t-4)(t^{2}-4)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[3])^(7) = -(1)/(720)*t*((t)^(2)- 1)*(t + 3)*(t - 4)*((t)^(2)- 4)
 
(Subscript[A, 3])^(7) == -Divide[1,720]*t*((t)^(2)- 1)*(t + 3)*(t - 4)*((t)^(2)- 4)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex37 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{4}^{7} = \tfrac{1}{5040}t(t^{2}-1)(t^{2}-4)(t^{2}-9)}
A_{4}^{7} = \tfrac{1}{5040}t(t^{2}-1)(t^{2}-4)(t^{2}-9)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(A[4])^(7) = (1)/(5040)*t*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)
 
(Subscript[A, 4])^(7) == Divide[1,5040]*t*((t)^(2)- 1)*((t)^(2)- 4)*((t)^(2)- 9)
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex38 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = f_{0}}
f = f_{0}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
f = f[0]
 
f == Subscript[f, 0]
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex39 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = ({[z_{1}]}f-{[z_{0}]}f)/(z_{1}-z_{0})}
f = ({[z_{1}]}f-{[z_{0}]}f)/(z_{1}-z_{0})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
f = ((z[1])*f -(z[0])*f)/(z[1]- z[0])
 
f == ((Subscript[z, 1])*f -(Subscript[z, 0])*f)/(Subscript[z, 1]- Subscript[z, 0])
 Skipped - no semantic math Skipped - no semantic math - -
3.3#Ex40 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = ({[z_{1},z_{2}]}f-{[z_{0},z_{1}]}f)/(z_{2}-z_{0})}
f = ({[z_{1},z_{2}]}f-{[z_{0},z_{1}]}f)/(z_{2}-z_{0})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
f = ([z[1], z[2]]*f -[z[0], z[1]]*f)/(z[2]- z[0])
 
f == ([Subscript[z, 1], Subscript[z, 2]]*f -[Subscript[z, 0], Subscript[z, 1]]*f)/(Subscript[z, 2]- Subscript[z, 0])
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E39 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(f) = [f_{0}]x+(f-f_{0})[f_{0},f_{1}]x+(f-f_{0})(f-f_{1})[f_{0},f_{1},f_{2}]x}
x(f) = [f_{0}]x+(f-f_{0})[f_{0},f_{1}]x+(f-f_{0})(f-f_{1})[f_{0},f_{1},f_{2}]x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
x(f) = (f[0])*x(+)*(f - f[0])*[f[0], f[1]]*x(+)*(f - f[0])*(f - f[1])*[f[0], f[1], f[2]]*x
 
x[f] == (Subscript[f, 0])*x[+]*(f - Subscript[f, 0])*[Subscript[f, 0], Subscript[f, 1]]*x[+]*(f - Subscript[f, 0])*(f - Subscript[f, 1])*[Subscript[f, 0], Subscript[f, 1], Subscript[f, 2]]*x
 Skipped - no semantic math Skipped - no semantic math - -
3.3.E40 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = -2.2+1.44011\;1973(f-0.09614\;53780)+0.08865\;85832\*(f-0.09614\;53780)(f-0.02670\;63331)}
x = -2.2+1.44011\;1973(f-0.09614\;53780)+0.08865\;85832\*(f-0.09614\;53780)(f-0.02670\;63331)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
x = - 2.2 + 1.440111973*(f - 0.0961453780)+ 0.0886585832 *(f - 0.0961453780)*(f - 0.0267063331)
 
x == - 2.2 + 1.440111973*(f - 0.0961453780)+ 0.0886585832 *(f - 0.0961453780)*(f - 0.0267063331)
 Skipped - no semantic math Skipped - no semantic math - -
Retrieved from "https://lct.wmflabs.org/w/index.php?title=3.3&oldid=58069"