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Bateman Function

k_nu(x)=(e^(-x))/(Gamma(1+1/2nu))U(-1/2nu,0,2x)

for x>0, where U is a confluent hypergeometric function of the second kind.

See also

Confluent Hypergeometric Differential Equation, Hypergeometric Function

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References

Bateman, H. "The k-Function, a Particular Case of the Confluent Hypergeometric Function." Trans. Amer. Math. Soc. 33, 817-831, 1931.Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 179, 1998.Koepf, W. and Schmersau, D. "Bounded Nonvanishing Functions are Bateman Functions." Complex Variables 25, 237-259, 1994.

Referenced on Wolfram|Alpha

Bateman Function

Cite this as:

Weisstein, Eric W. "Bateman Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BatemanFunction.html

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