Formula:4370

Digital Library of Mathematical Functions ID 10.47.E5

${\displaystyle{\displaystyle{\mathsf{h}^{(1)}_{n}}\left(z\right)=\sqrt{\tfrac{1}{2}\pi/z}{H^{(1)}_{n+\frac{1}{2}}}\left(z\right)=(-1)^{n+1}\mathrm{i}\sqrt{\tfrac{1}{2}\pi/z}{H^{(1)}_{-n-\frac{1}{2}}}\left(z\right),}}$

Symbols List

• ${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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