Bateman function: Difference between revisions

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In mathematics, the '''Bateman function''' (or ''k''-function) is a special case of the [[confluent hypergeometric function]] studied by [[Harry Bateman]](1931).<ref>{{Citation | last1=Bateman | first1=H. | authorlink=Harry Bateman | title=The k-function, a particular case of the confluent hypergeometric function | doi=10.2307/1989510 | mr=1501618 | year=1931 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=33 | issue=4 | pages=817–831}}</ref><ref>{{Springer|id=B/b015360|title=Bateman function}}</ref>. Bateman defined it by

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