Formula:4475

Digital Library of Mathematical Functions ID 10.60.E3

${\displaystyle{\displaystyle\frac{e^{-w}}{w}=\frac{2}{\pi}\sum_{n=0}^{\infty}(2n+1){\mathsf{i}^{(1)}_{n}}\left(v\right)\mathsf{k}_{n}\left(u\right)P_{n}\left(\cos\alpha\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|ve^{\pm i\alpha}|<|u|}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}\left(z\right)}}$:
• ${\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}$: modified spherical Bessel function
• ${\displaystyle{\displaystyle n}}$: integer
 

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