Formula:4270

Digital Library of Mathematical Functions ID 10.39.E5

${\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu}e^{\pm z}}{\Gamma\left(\nu+1\right)}M\left(\nu+\tfrac{1}{2},2\nu+1,\mp 2z\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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