Formula:3365

Digital Library of Mathematical Functions ID 8.18.E1

${\displaystyle{\displaystyle I_{x}\left(a,b\right)={\Gamma\left(a+b\right)x^{a}(1-x)^{b-1}}\*\left(\sum_{k=0}^{n-1}\frac{1}{\Gamma\left(a+k+1\right)\Gamma\left(b-k\right)}\left(\frac{x}{1-x}\right)^{k}+O\left(\frac{1}{\Gamma\left(a+n+1\right)}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}$: incomplete beta function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle b}}$: parameter
• ${\displaystyle{\displaystyle x}}$: variable
 

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