Formula:4571

Digital Library of Mathematical Functions ID 10.68.E8

${\displaystyle{\displaystyle\operatorname{ber}_{\nu}'x=\tfrac{1}{2}M_{\nu+1}\cos\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)-\tfrac{1}{2}M_{\nu-1}\cos\left(\theta_{\nu-1}-\tfrac{1}{4}\pi\right)=(\nu/x)M_{\nu}\cos\theta_{\nu}+M_{\nu+1}\cos\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)=-(\nu/x)M_{\nu}\cos\theta_{\nu}-M_{\nu-1}\cos\left(\theta_{\nu-1}-\tfrac{1}{4}\pi\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}$: modulus of Bessel functions
• ${\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}$: phase of Bessel functions
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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