Formula:4487

Digital Library of Mathematical Functions ID 10.61.E1

${\displaystyle{\displaystyle\operatorname{ber}_{\nu}x+i\operatorname{bei}_{\nu}x=J_{\nu}\left(xe^{3\pi i/4}\right)=e^{\nu\pi i}J_{\nu}\left(xe^{-\pi i/4}\right)=e^{\nu\pi i/2}I_{\nu}\left(xe^{\pi i/4}\right)=e^{3\nu\pi i/2}I_{\nu}\left(xe^{-3\pi i/4}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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