Formula:7020

Digital Library of Mathematical Functions ID 19.16.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Carlsonmultivarhyper{-a}@{\mathbf{b}}{\mathbf{z}}=\frac{1}{\EulerBeta@{a}{a^{\prime}}}\int_{0}^{\infty}t^{a^{\prime}-1}\prod^{n}_{j=1}(t+z_{j})^{-b_{j}}\diff{t}=\frac{1}{\EulerBeta@{a}{a^{\prime}}}\int_{0}^{\infty}t^{a-1}\prod^{n}_{j=1}(1+tz_{j})^{-b_{j}}\diff{t},}

Constraint(s)

${\displaystyle{\displaystyle b_{j}\in\mathbb{R}}}$
${\displaystyle{\displaystyle z_{j}\in\mathbb{C}\setminus(-\infty,0]}}$
${\displaystyle{\displaystyle b_{1}+\cdots+b_{n}>a>0}}$
${\displaystyle{\displaystyle b_{j}\in\mathbb{R}}}$
${\displaystyle{\displaystyle z_{j}\in\mathbb{C}\setminus(-\infty,0]}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$: beta function
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$:
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle\setminus}}$:
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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