Formula:4186

Digital Library of Mathematical Functions ID 10.25.E2

${\displaystyle{\displaystyle I_{\nu}\left(z\right)=(\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\Gamma\left(\nu+k+1\right)}.}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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