Formula:3878

Digital Library of Mathematical Functions ID 10.17.E11

${\displaystyle{\displaystyle{H^{(1)}_{\nu}}'\left(z\right)\sim i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{i\omega}\sum_{k=0}^{\infty}i^{k}\frac{b_{k}(\nu)}{z^{k}},}}$

Constraint(s)

${\displaystyle{\displaystyle-\pi+\delta\leq\operatorname{ph}z\leq 2\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$: Bessel function of the third kind (or Hankel function)
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
• ${\displaystyle{\displaystyle\omega}}$: 10.17.E2
• ${\displaystyle{\displaystyle b_{k}(\nu)}}$: expansion (locally)
 

Resources that cite this formula

No records found.