Formula:5873

Digital Library of Mathematical Functions ID 15.14.E1

${\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}\mathbf{F}\left({a,b\atop c};-x\right)\mathrm{d}x=\frac{\Gamma\left(s\right)\Gamma\left(a-s\right)\Gamma\left(b-s\right)}{\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-s\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: Olver’s hypergeometric function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle b}}$: real or complex parameter
• ${\displaystyle{\displaystyle c}}$: real or complex parameter
 

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