Formula:4349

Digital Library of Mathematical Functions ID 10.44.E4

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \left(\tfrac{1}{2}z\right)^{\nu}=\sum_{k=0}^{\infty}(-1)^{k}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\modBesselI{\nu+2k}@{z},}

Constraint(s)

${\displaystyle{\displaystyle\nu\neq 0,-1,-2,\ldots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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