DLMF:10.14.E6

MaRDI QIDQ3841

• Label: DLMF:10.14.E6

Digital Library of Mathematical Functions ID 10.14.E6

${\displaystyle{\displaystyle|J_{\nu}'\left(\nu x\right)|\leq\frac{(1+x^{2})^{\frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\frac{x^{\nu}\exp\left(\nu(1-x^{2})^{\frac{1}{2}}\right)}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}},}}$

Constraint(s)

${\displaystyle{\displaystyle\nu>0,0<x\leq 1}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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