Formula:4539

Digital Library of Mathematical Functions ID 10.65.E9

${\displaystyle{\displaystyle\left(\operatorname{ber}_{\nu}'x\right)^{2}+\left(\operatorname{bei}_{\nu}'x\right)^{2}=(\tfrac{1}{2}x)^{2\nu-2}\sum_{k=0}^{\infty}\frac{2k^{2}+2\nu k+\frac{1}{4}\nu^{2}}{\Gamma\left(\nu+k+1\right)\Gamma\left(\nu+2k+1\right)}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}.}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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