Formula:3347

Digital Library of Mathematical Functions ID 8.17.E9

${\displaystyle{\displaystyle\mathrm{B}_{x}\left(a,b\right)=\frac{x^{a}(1-x)^{b-1}}{a}F\left({1,1-b\atop a+1};\frac{x}{x-1}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{B}_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}$: incomplete beta function
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle b}}$: parameter
• ${\displaystyle{\displaystyle x}}$: variable
 

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