Formula:3375

Digital Library of Mathematical Functions ID 8.18.E9

${\displaystyle{\displaystyle I_{x}\left(a,b\right)\sim\tfrac{1}{2}\operatorname{erfc}\left(-\eta\sqrt{b/2}\right)+\frac{1}{\sqrt{2\pi(a+b)}}\*\left(\frac{x}{x_{0}}\right)^{a}\left(\frac{1-x}{1-x_{0}}\right)^{b}\sum_{k=0}^{\infty}\frac{(-1)^{k}c_{k}(\eta)}{(a+b)^{k}},}}$

Symbols List

• ${\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}$: incomplete beta function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle b}}$: parameter
• ${\displaystyle{\displaystyle x}}$: variable
• ${\displaystyle{\displaystyle c_{k}(\eta)}}$: coefficients
 

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