gives the Hankel function of the first kind .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- is given by .
- HankelH1[n,z] has a branch cut discontinuity in the complex z plane running from to .
- For certain special arguments, HankelH1 automatically evaluates to exact values.
- HankelH1 can be evaluated to arbitrary numerical precision.
- HankelH1 automatically threads over lists.
- HankelH1 can be used with a CenteredInterval object. »
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (6)
Specific Values (4)
Function Properties (7)
HankelH1 is not injective over complexes:
Use FindInstance to find inputs that demonstrate it is not injective:
Compute the indefinite integral using Integrate:
Series Expansions (6)
Find the Taylor expansion using Series:
General term in the series expansion using SeriesCoefficient:
Asymptotic approximation of HankelH1:
HankelH1 can be applied to a power series:
There can be subtleties with asymptotic approximation when the function to be approximated approaches zero infinitely many times in every neighborhood of the approximation point. As an example, consider the asymptotic expansion of near :
Properties & Relations (2)
Wolfram Research (2007), HankelH1, Wolfram Language function, https://reference.wolfram.com/language/ref/HankelH1.html.
Wolfram Language. 2007. "HankelH1." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HankelH1.html.
Wolfram Language. (2007). HankelH1. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HankelH1.html