DLMF:18.15.E6 (Q5696): Difference between revisions

Revision as of 15:37, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:18.15.E6	No description defined

{\displaystyle{\displaystyle(\sin\tfrac{1}{2}\theta)^{\alpha+\frac{1}{2}}(\cos% \tfrac{1}{2}\theta)^{\beta+\frac{1}{2}}P^{(\alpha,\beta)}_{n}\left(\cos\theta% \right)=\frac{\Gamma\left(n+\alpha+1\right)}{2^{\frac{1}{2}}\rho^{\alpha}n!}\*% \left(\theta^{\frac{1}{2}}J_{\alpha}\left(\rho\theta\right)\sum_{m=0}^{M}% \dfrac{A_{m}(\theta)}{\rho^{2m}}+\theta^{\frac{3}{2}}J_{\alpha+1}\left(\rho% \theta\right)\sum_{m=0}^{M-1}\dfrac{B_{m}(\theta)}{\rho^{2m+1}}+\varepsilon_{M% }(\rho,\theta)\right),}}

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DLMF:18.15.E6

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{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2adec

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

C5.S2.E1.m2adec

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{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2aadec

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@@ Property / Symbols used @@
+Q11660
@@ Property / Symbols used: Q11660 / rank @@
+Normal rank
@@ Property / Symbols used: Q11660 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}$ 
\JacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}
@@ Property / Symbols used: Q11660 / qualifier @@
+xml-id: C18.S3.T1.t1.r2.m2aadec