Formula:3247

Digital Library of Mathematical Functions ID 8.8.E17

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}(e^{z}\gamma\left(a,z\right))=(-1)^{n}{\left(1-a\right)_{n}}e^{z}\gamma\left(a-n,z\right),}}$

Symbols List

• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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