Formula:3839

Digital Library of Mathematical Functions ID 10.14.E4

${\displaystyle{\displaystyle|J_{\nu}\left(z\right)|\leq\frac{|\tfrac{1}{2}z|^{\nu}e^{|\Im z|}}{\Gamma\left(\nu+1\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\nu\geq-\frac{1}{2}}}$

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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\Im}}$: imaginary part
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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