Difference between revisions of "Hankel H (2) in terms of csc and Bessel J"
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(Created page with "==Theorem== The following formula holds: $$H_{\nu}^{(2)}(z)=i\csc(\nu \pi) \left[ J_{-\nu}(z)-e^{\nu \pi i}J_{\nu}(z) \right],$$ where $H_{\nu}^{(2)}$ denotes the Hankel H (...") |
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Revision as of 04:47, 11 June 2016
Theorem
The following formula holds: $$H_{\nu}^{(2)}(z)=i\csc(\nu \pi) \left[ J_{-\nu}(z)-e^{\nu \pi i}J_{\nu}(z) \right],$$ where $H_{\nu}^{(2)}$ denotes the Hankel function of the second kind, $i$ denotes the imaginary number, $\csc$ denotes the cosecant, $J_{-\nu}$ denotes the Bessel function of the first kind, and $e^{\nu \pi i}$ denotes the exponential.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): 9.1.4
