DLMF:18.18.E15 (Q5805)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:18.18.E15	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(\frac{1+x}{2}\right)^{n}=\frac{{\left(\beta+% 1\right)_{n}}}{{\left(\alpha+\beta+2\right)_{n}}}\sum_{\ell=0}^{n}\frac{\alpha% +\beta+2\ell+1}{\alpha+\beta+1}\frac{{\left(\alpha+\beta+1\right)_{\ell}}{% \left(n-\ell+1\right)_{\ell}}}{{\left(\beta+1\right)_{\ell}}{\left(n+\alpha+% \beta+2\right)_{\ell}}}P^{(\alpha,\beta)}_{\ell}\left(x\right),}}

0 references

DLMF:18.18.E15

0 references

Defining formula

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

C18.S3.T1.t1.r2.m2addec

0 references

Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1acdec

0 references

Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1edec

0 references

Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1ndec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1kdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5805&oldid=31177"