DLMF:18.17.E36 (Q5777): Difference between revisions

Revision as of 01:13, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.17.E36	No description defined

{\displaystyle{\displaystyle\int_{-1}^{1}(1-x)^{z-1}(1+x)^{\beta}P^{(\alpha,% \beta)}_{n}\left(x\right)\mathrm{d}x=\frac{2^{\beta+z}\Gamma\left(z\right)% \Gamma\left(1+\beta+n\right){\left(1+\alpha-z\right)_{n}}}{n!\Gamma\left(1+% \beta+z+n\right)},}}

0 references

DLMF:18.17.E36

0 references

{\displaystyle{\displaystyle\Re z>0}}

0 references

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

C5.S2.E1.m2andec

0 references

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

C18.S3.T1.t1.r2.m2afdec

0 references

@@ 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.m2afdec