Formula:4572

Digital Library of Mathematical Functions ID 10.68.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Kelvinbei{\nu}'@@{x}=\tfrac{1}{2}\HankelmodM{\nu+1}\sin@{\Hankelphasetheta{\nu+1}-\tfrac{1}{4}\pi}-\tfrac{1}{2}\HankelmodM{\nu-1}\sin@{\Hankelphasetheta{\nu-1}-\tfrac{1}{4}\pi}=(\nu/x)\HankelmodM{\nu}\sin@@{\Hankelphasetheta{\nu}}+\HankelmodM{\nu+1}\sin@{\Hankelphasetheta{\nu+1}-\tfrac{1}{4}\pi}=-(\nu/x)\HankelmodM{\nu}\sin@@{\Hankelphasetheta{\nu}}-\HankelmodM{\nu-1}\sin@{\Hankelphasetheta{\nu-1}-\tfrac{1}{4}\pi}.}

Symbols List

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

Resources that cite this formula

No records found.