Bateman function

In mathematics, the Bateman function (or k-function) k_n is a special case of the confluent hypergeometric function studied by Bateman (1931). Bateman defined it by

$\displaystyle k_n(x) = \frac{2}{\pi}\int_0^{\pi/2}\cos(x\tan\theta-n\theta) \, d\theta$

This is not to be confused with another function of the same name which is used in Pharmacokinetics.

References

• Bateman, H. (1931), "The k-function, a particular case of the confluent hypergeometric function", Transactions of the American Mathematical Society 33 (4): 817–831, doi:10.2307/1989510, ISSN 0002-9947, MR 1501618
• Hazewinkel, Michiel, ed. (2001), "Bateman function", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4