Formula:4504

Digital Library of Mathematical Functions ID 10.61.E12

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

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
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle x}}$: real variable
 

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