DLMF:19.31.E2 (Q6690)

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Language	Label	Description	Also known as
English	DLMF:19.31.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{{\mathbb{R}^{n}}}(\mathbf{x}^{\mathrm{T}}% \mathbf{A}\mathbf{x})^{\mu}\exp\left(-\mathbf{x}^{\mathrm{T}}\mathbf{B}\mathbf% {x}\right)\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}=\frac{\pi^{n/2}\Gamma\left(\mu+% \tfrac{1}{2}n\right)}{\sqrt{\det\mathbf{B}}\Gamma\left(\tfrac{1}{2}n\right)}R_% {\mu}\left(\tfrac{1}{2},\dots,\tfrac{1}{2};\lambda_{1},\dots,\lambda_{n}\right% ),}}

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DLMF:19.31.E2

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{\displaystyle{\displaystyle\mu>-\tfrac{1}{2}n}}

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multivariate hypergeometric function

Defining formula

{\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}

C19.S16.E9.m2adec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\det}}

C1.S3.SS1.m1adec

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Defining formula

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

C1.S4.SS4.m1adec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.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 n}}

C19.S1.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle\lambda_{n}}}

C19.S31.XMD1.m1dec

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Sitelinks

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