Formula:4194

Digital Library of Mathematical Functions ID 10.27.E7

${\displaystyle{\displaystyle I_{\nu}\left(z\right)=\tfrac{1}{2}e^{\mp\nu\pi i/2}\left({H^{(1)}_{\nu}}\left(ze^{\pm\pi i/2}\right)+{H^{(2)}_{\nu}}\left(ze^{\pm\pi i/2}\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-\pi\leq\pm\operatorname{ph}z\leq\tfrac{1}{2}\pi}}$

Symbols List

• ${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: 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
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

Resources that cite this formula

No records found.