Formula:4166

Digital Library of Mathematical Functions ID 10.23.E15

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

Constraint(s)

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

Symbols List

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

Resources that cite this formula

No records found.