Formula:3229

Digital Library of Mathematical Functions ID 8.7.E5

${\displaystyle{\displaystyle\gamma^{*}\left(a,z\right)=e^{-\frac{1}{2}z}\sum_{n=0}^{\infty}\frac{{\left(1-a\right)_{n}}}{\Gamma\left(n+a+1\right)}{\left(2n+1\right)}{\mathsf{i}^{(1)}_{n}}\left(\tfrac{1}{2}z\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}$: incomplete gamma function
• ${\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: parameter
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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