DLMF:35.7.E3 (Q9814)

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Language	Label	Description	Also known as
English	DLMF:35.7.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{{}_{2}F_{1}}\left({a,b\atop c};\begin{bmatrix}t_{% 1}&0\\ 0&t_{2}\end{bmatrix}\right)=\sum_{k=0}^{\infty}\frac{{\left(a\right)_{k}}{% \left(c-a\right)_{k}}{\left(b\right)_{k}}{\left(c-b\right)_{k}}}{k!\,{\left(c% \right)_{2k}}{\left(c-\tfrac{1}{2}\right)_{k}}}\*(t_{1}t_{2})^{k}{{}_{2}F_{1}}% \left({a+k,b+k\atop c+2k};t_{1}+t_{2}-t_{1}t_{2}\right).}}

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DLMF:35.7.E3

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generalized hypergeometric function of matrix argument

Defining formula

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

C35.S8.E1.m2abdec

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Defining formula

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

C5.S2.SS3.m1adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5aadec

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Defining formula

{\displaystyle{\displaystyle a}}

C35.S1.XMD1.m1adec

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Defining formula

{\displaystyle{\displaystyle t_{j}}}

C35.S1.XMD14.m1dec

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Defining formula

{\displaystyle{\displaystyle b}}

C35.S1.XMD2.m1adec

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Defining formula

{\displaystyle{\displaystyle c}}

C35.S1.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle k}}

C35.S1.XMD5.m1adec

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