DLMF:19.16.E9 (Q6324): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:19.16.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{1}% {\mathrm{B}\left(a,a^{\prime}\right)}\int_{0}^{\infty}t^{a^{\prime}-1}\prod^{n% }_{j=1}(t+z_{j})^{-b_{j}}\mathrm{d}t=\frac{1}{\mathrm{B}\left(a,a^{\prime}% \right)}\int_{0}^{\infty}t^{a-1}\prod^{n}_{j=1}(1+tz_{j})^{-b_{j}}\mathrm{d}t,}}

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DLMF:19.16.E9

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Symbols defined

multivariate hypergeometric function

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{\displaystyle{\displaystyle b_{j}\in\mathbb{R}}}

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{\displaystyle{\displaystyle z_{j}\in\mathbb{C}\setminus(-\infty,0]}}

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{\displaystyle{\displaystyle b_{1}+\cdots+b_{n}>a>0}}

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{\displaystyle{\displaystyle b_{j}\in\mathbb{R}}}

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{\displaystyle{\displaystyle z_{j}\in\mathbb{C}\setminus(-\infty,0]}}

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Defining formula

{\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

C5.S12.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathbb{C}}}

introduction.Sx4.p1.t1.r1.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aedec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aedec

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Defining formula

{\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}

introduction.Sx4.p2.t1.r1.m3adec

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Defining formula

{\displaystyle{\displaystyle\mathbb{R}}}

introduction.Sx4.p2.t1.r14.m2adec

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Defining formula

{\displaystyle{\displaystyle\setminus}}

introduction.Sx4.p2.t1.r19.m2adec

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Defining formula

{\displaystyle{\displaystyle n}}

C19.S1.XMD3.m1adec

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Sitelinks

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