Formula:3866

Digital Library of Mathematical Functions ID 10.16.E9

${\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu}}{\Gamma\left(\nu+1\right)}{{}_{0}F_{1}}\left(-;\nu+1;-\tfrac{1}{4}z^{2}\right).}}$

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
• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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