A Bessel function Neumann series is a series expansion of a function of a complex
variable 
in terms of Bessel
functions of the first kind, given by
 |
(1)
|
where 
is a real.
This use of the name is distinct from the Neumann series
of an operator.
Special cases include
 |
(2)
|
where 
is the gamma function, and
 |
(3)
|
where
 |
(4)
|
and 
is the floor function.
See also
Fourier-Bessel Series,
Generalized Fourier Series,
Kapteyn
Series,
Neumann Series
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References
Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge
University Press, 1966.Referenced on Wolfram|Alpha
Bessel Function Neumann Series
Cite this as:
Weisstein, Eric W. "Bessel Function Neumann
Series." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BesselFunctionNeumannSeries.html
Subject classifications
