DLMF:18.30.E5 (Q6003): Difference between revisions

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English	DLMF:18.30.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{(-1)^{n}{\left(\alpha+\beta+c+1\right)_{n}}n% !\,P^{(\alpha,\beta)}_{n}\left(x;c\right)}{{\left(\alpha+\beta+2c+1\right)_{n}% }{\left(\beta+c+1\right)_{n}}}=\sum_{\ell=0}^{n}\frac{{\left(-n\right)_{\ell}}% {\left(n+\alpha+\beta+2c+1\right)_{\ell}}}{{\left(c+1\right)_{\ell}}{\left(% \beta+c+1\right)_{\ell}}}\left(\tfrac{1}{2}x+\tfrac{1}{2}\right)^{\ell}\*{{}_{% 4}F_{3}}\left({\ell-n,n+\ell+\alpha+\beta+2c+1,\beta+c,c\atop\beta+\ell+c+1,% \ell+c+1,\alpha+\beta+2c};1\right),}}

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DLMF:18.30.E5

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Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}

C16.S2.m1adec

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Defining formula

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

C5.S2.SS3.m1adec

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associated Jacobi polynomial

Defining formula

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

C18.S30.E4.m2aadec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1dec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S30.XMD1.m1cdec

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Sitelinks

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