DLMF:15.9.E10 (Q5100)

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Language	Label	Description	Also known as
English	DLMF:15.9.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{(\lambda)}_{n}\left(x;\phi\right)=\frac{{\left% (2\lambda\right)_{n}}}{n!}e^{n\mathrm{i}\phi}F\left({-n,\lambda+\mathrm{i}x% \atop 2\lambda};1-e^{-2\mathrm{i}\phi}\right).}}

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DLMF:15.9.E10

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$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

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

C15.S2.E1.m2aidec

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Defining formula

{\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{\phi}\right)}}

C18.S19.Px3.p1.m2adec

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Defining formula

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

C5.S2.SS3.m1addec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2aadec

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