DLMF:5.12.E4

MaRDI QIDQ2847

• Label: DLMF:5.12.E4

Digital Library of Mathematical Functions ID 5.12.E4

${\displaystyle{\displaystyle\int_{0}^{1}\frac{t^{a-1}(1-t)^{b-1}}{(t+z)^{a+b}}\mathrm{d}t=\mathrm{B}\left(a,b\right)(1+z)^{-a}z^{-b},}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$: beta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex variable
• ${\displaystyle{\displaystyle b}}$: real or complex variable
 

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