Formula:4591

Digital Library of Mathematical Functions ID 10.69.E3

${\displaystyle{\displaystyle\operatorname{ker}_{\nu}\left(\nu x\right)+i\operatorname{kei}_{\nu}\left(\nu x\right)\sim e^{-\nu\xi}\left(\frac{\pi}{2\nu\xi}\right)^{\ifrac{1}{2}}\left(\frac{xe^{3\pi i/4}}{1+\xi}\right)^{-\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{U_{k}(\xi^{-1})}{\nu^{k}},}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: 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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle U_{k}(p)}}$: polynomial coefficient
• ${\displaystyle{\displaystyle\xi}}$: 10.69.E1
 

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