Formula:3299

Digital Library of Mathematical Functions ID 8.12.E6

${\displaystyle{\displaystyle z^{-a}\gamma^{*}\left(-a,-z\right)=\cos\left(\pi a\right)-2\sin\left(\pi a\right)\left(\frac{e^{\frac{1}{2}a\eta^{2}}}{\sqrt{\pi}}F\left(\eta\sqrt{a/2}\right)+T(a,\eta)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{z}\right)}}$: 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
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle\eta(\lambda)}}$: η ( λ )
• ${\displaystyle{\displaystyle T(a,\eta)}}$: function
 

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