Formula:4540

Digital Library of Mathematical Functions ID 10.66.E1

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x}=\sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!}=\sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}\modBesselI{\nu+k}@{x}}{2^{k/2}k!}.}

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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