@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\mu\neq\frac{1}{2},\frac{3}{2},\frac{5}{2},\ldots}}$ 
\mu\neq\frac{1}{2},\frac{3}{2},\frac{5}{2},\ldots
+Normal rank
@@ Property / Symbols used @@
+gamma function
@@ Property / Symbols used: gamma function / rank @@
+Normal rank
@@ Property / Symbols used: gamma function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 
\EulerGamma@{\NVar{z}}
@@ Property / Symbols used: gamma function / qualifier @@
+xml-id: C5.S2.E1.m2adec
@@ Property / Symbols used @@
+Q11481
@@ Property / Symbols used: Q11481 / rank @@
+Normal rank
@@ Property / Symbols used: Q11481 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: Q11481 / qualifier @@
+xml-id: C14.S21.SS1.p1.m1adec
@@ Property / Symbols used @@
+the ratio of the circumference of a circle to its diameter
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\pi}}$ 
\cpi
+xml-id: C3.S12.E1.m2adec
@@ 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 @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2adec
@@ Property / Symbols used @@
+hyperbolic cosine function
@@ Property / Symbols used: hyperbolic cosine function / rank @@
+Normal rank
@@ Property / Symbols used: hyperbolic cosine function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ 
\cosh@@{\NVar{z}}
@@ Property / Symbols used: hyperbolic cosine function / qualifier @@
+xml-id: C4.S28.E2.m2aadec
@@ Property / Symbols used @@
+$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$  Olver’s hypergeometric function
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}$ 
\hyperOlverF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
+xml-id: C15.S2.E2.m2adec
@@ Property / Symbols used @@
+Q11591
@@ Property / Symbols used: Q11591 / rank @@
+Normal rank
@@ Property / Symbols used: Q11591 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mu}}$ 
\mu
@@ Property / Symbols used: Q11591 / qualifier @@
+xml-id: C14.S1.XMD7.m1dec
@@ Property / Symbols used @@
+Q11590
@@ Property / Symbols used: Q11590 / rank @@
+Normal rank
@@ Property / Symbols used: Q11590 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q11590 / qualifier @@
+xml-id: C14.S1.XMD8.m1dec
@@ Property / Symbols used @@
+Q11626
@@ Property / Symbols used: Q11626 / rank @@
+Normal rank
@@ Property / Symbols used: Q11626 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\xi>0}}$ 
\xi>0
@@ Property / Symbols used: Q11626 / qualifier @@
+xml-id: C14.S19.XMD7.m1dec

DLMF:14.19.E2 (Q4914): Difference between revisions

μ ≠ 1 2 , 3 2 , 5 2 , … 𝜇 1 2 3 2 5 2 … {\displaystyle{\displaystyle\mu\neq\frac{1}{2},\frac{3}{2},\frac{5}{2},\ldots}}

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

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

π {\displaystyle{\displaystyle\pi}}

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

cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

𝐅 ⁡ ( a , b ; c ; z ) scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

μ 𝜇 {\displaystyle{\displaystyle\mu}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

ξ > 0 𝜉 0 {\displaystyle{\displaystyle\xi>0}}

Latest revision as of 13:29, 2 January 2020

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${\displaystyle{\displaystyle\mu\neq\frac{1}{2},\frac{3}{2},\frac{5}{2},\ldots}}$

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

${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

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

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

${\displaystyle{\displaystyle\cosh\NVar{z}}}$

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

${\displaystyle{\displaystyle\mu}}$

${\displaystyle{\displaystyle\nu}}$

${\displaystyle{\displaystyle\xi>0}}$