Formula:4550

Digital Library of Mathematical Functions ID 10.67.E8

${\displaystyle{\displaystyle\operatorname{bei}_{\nu}'x\sim\frac{e^{x/\sqrt{2}}}{(2\pi x)^{\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{b_{k}(\nu)}{x^{k}}\sin\left(\frac{x}{\sqrt{2}}+\left(\frac{\nu}{2}+\frac{3k}{4}+\frac{1}{8}\right)\pi\right)+\frac{1}{\pi}(\cos\left(2\nu\pi\right)\operatorname{ker}_{\nu}'x-\sin\left(2\nu\pi\right)\operatorname{kei}_{\nu}'x).}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: 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
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle b_{k}(\nu)}}$: expansion (locally)
 

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