Formula:3367

Digital Library of Mathematical Functions ID 8.18.E3

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

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
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle b}}$: parameter
• ${\displaystyle{\displaystyle x}}$: variable
• ${\displaystyle{\displaystyle F_{k}}}$: functions
• ${\displaystyle{\displaystyle d_{k}}}$: coefficients
 

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