Hankel Function
المؤلف:
Arfken, G.
المصدر:
"Hankel Functions." §11.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press
الجزء والصفحة:
...
24-3-2019
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Hankel Function
There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) which is a linear combination of Bessel functions of the first and second kinds.
Another type of Hankel function is defined by the contour integral
for ![I[w]<0](http://mathworld.wolfram.com/images/equations/HankelFunction/Inline1.gif)
, 
, 
, where 
is a Hankel contour. The Riemann zeta function can be expressed in terms of 
as
for 
and ![R[z]>1](http://mathworld.wolfram.com/images/equations/HankelFunction/Inline7.gif)
, where 
is the gamma function (Krantz 1999, p. 160).
REFERENCES:
Arfken, G. "Hankel Functions." §11.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 604-610, 1985.
Hankel, H. "Die Cylinderfunctionen erster und zweiter Art." Math. Ann. 1, 467-501, 1869.
Hankel, H. "Bestimmte Integrale mit Cylinderfunctionen." Math. Ann. 8, 453-470, 1875.
Krantz, S. G. "The Hankel Contour and Hankel Functions." §13.2.4 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 159, 1999.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 623-624, 1953.A
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