Formula:4398

Digital Library of Mathematical Functions ID 10.49.E7

${\displaystyle{\displaystyle{\mathsf{h}^{(2)}_{n}}\left(z\right)=e^{-iz}\sum_{k=0}^{n}(-i)^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle{\mathsf{h}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}$: spherical Bessel function of the third kind
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a_{k}(\nu)}}$: expansion (locally)
 

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