Formula:3282

Digital Library of Mathematical Functions ID 8.11.E11

${\displaystyle{\displaystyle\gamma^{*}\left(1-a,-x\right)=x^{a-1}\left(-\cos\left(\pi a\right)+\frac{\sin\left(\pi a\right)}{\pi}\left(2\sqrt{\pi}F\left(y\right)+\frac{2}{3}\sqrt{\frac{2\pi}{a}}\left(1-y^{2}\right)\right)e^{y^{2}}+O\left(a^{-1}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle F\left(\NVar{z}\right)}}$: Dawson’s integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle y}}$: change of variable
 

Resources that cite this formula

No records found.