DLMF:13.2.E23 (Q4313): Difference between revisions

@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}$ 
\abs{\phase@@{z}}\leq\frac{1}{2}\pi-\delta
+Normal rank
@@ Property / Symbols used @@
+gamma function
@@ Property / Symbols used: gamma function / rank @@
+Normal rank
@@ Property / Symbols used: gamma function / qualifier @@
+test:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 
\EulerGamma@{\NVar{z}}
@@ Property / Symbols used: gamma function / qualifier @@
+xml-id: C5.S2.E1.m2aldec
@@ Property / Symbols used @@
+Olver’s confluent hypergeometric function
@@ Property / Symbols used: Olver’s confluent hypergeometric function / rank @@
+Normal rank
+test:  ${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}$ 
\OlverconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
+xml-id: C13.S2.E3.m2addec
@@ Property / Symbols used @@
+asymptotic equality
@@ Property / Symbols used: asymptotic equality / rank @@
+Normal rank
@@ Property / Symbols used: asymptotic equality / qualifier @@
+test:  ${\displaystyle{\displaystyle\sim}}$ 
\asympeq
@@ Property / Symbols used: asymptotic equality / qualifier @@
+xml-id: C2.S1.E1.m2aadec
@@ Property / Symbols used @@
+the ratio of the circumference of a circle to its diameter
+Normal rank
+test:  ${\displaystyle{\displaystyle\pi}}$ 
\cpi
+xml-id: C3.S12.E1.m2abdec
@@ Property / Symbols used @@
+base of natural logarithm
@@ Property / Symbols used: base of natural logarithm / rank @@
+Normal rank
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+test:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2aadec
@@ Property / Symbols used @@
+Q10817
@@ Property / Symbols used: Q10817 / rank @@
+Normal rank
@@ Property / Symbols used: Q10817 / qualifier @@
+test:  ${\displaystyle{\displaystyle\operatorname{ph}}}$ 
\phase
@@ Property / Symbols used: Q10817 / qualifier @@
+xml-id: C1.S9.E7.m1aadec
@@ Property / Symbols used @@
+Q11557
@@ Property / Symbols used: Q11557 / rank @@
+Normal rank
@@ Property / Symbols used: Q11557 / qualifier @@
+test:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11557 / qualifier @@
+xml-id: C13.S1.XMD6.m1vdec
@@ Property / Symbols used @@
+Q11560
@@ Property / Symbols used: Q11560 / rank @@
+Normal rank
@@ Property / Symbols used: Q11560 / qualifier @@
+test:  ${\displaystyle{\displaystyle\delta}}$ 
\delta
@@ Property / Symbols used: Q11560 / qualifier @@
+xml-id: C13.S1.XMD7.m1adec

DLMF:13.2.E23 (Q4313): Difference between revisions

${\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}$

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}$

${\displaystyle{\displaystyle\sim}}$

${\displaystyle{\displaystyle\pi}}$

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\operatorname{ph}}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle\delta}}$

Latest revision as of 14:38, 2 January 2020

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DLMF:13.2.E23 (Q4313): Difference between revisions

| ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

𝐌 ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

π {\displaystyle{\displaystyle\pi}}

e {\displaystyle{\displaystyle\mathrm{e}}}

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

z 𝑧 {\displaystyle{\displaystyle z}}

δ 𝛿 {\displaystyle{\displaystyle\delta}}

Latest revision as of 14:38, 2 January 2020

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${\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}$

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}$

${\displaystyle{\displaystyle\sim}}$

${\displaystyle{\displaystyle\pi}}$

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\operatorname{ph}}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle\delta}}$