Formula:4547

Digital Library of Mathematical Functions ID 10.67.E5

${\displaystyle{\displaystyle\operatorname{ker}_{\nu}'x\sim-e^{-x/\sqrt{2}}\left(\frac{\pi}{2x}\right)^{\frac{1}{2}}\sum_{k=0}^{\infty}\frac{b_{k}(\nu)}{x^{k}}\*\cos\left(\frac{x}{\sqrt{2}}+\left(\frac{\nu}{2}+\frac{k}{4}-\frac{1}{8}\right)\pi\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle b_{k}(\nu)}}$: expansion (locally)
 

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