Formula:4182

Digital Library of Mathematical Functions ID 10.24.E7

${\displaystyle{\displaystyle\widetilde{J}_{\nu}\left(x\right)=\left(\frac{2\tanh\left(\frac{1}{2}\pi\nu\right)}{\pi\nu}\right)^{\frac{1}{2}}\cos\left(\nu\ln\left(\tfrac{1}{2}x\right)-\gamma_{\nu}\right)+O\left(x^{2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\widetilde{J}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Bessel function of imaginary order
• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\tanh\NVar{z}}}$: hyperbolic tangent function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle\gamma_{\nu}}}$: parameter
 

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