Formula:4503

Digital Library of Mathematical Functions ID 10.61.E11

${\displaystyle{\displaystyle\operatorname{ker}_{\frac{1}{2}}\left(x\sqrt{2}\right)=\operatorname{kei}_{-\frac{1}{2}}\left(x\sqrt{2}\right)=-2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\sin\left(x-\frac{\pi}{8}\right),}}$

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
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle x}}$: real variable
 

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