Bateman function: Difference between revisions

Revision as of 15:07, 16 December 2023

Revision as of 15:09, 16 December 2023

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==Havelock function==

Complementary to the Bateman function, one may also define the Havelock function, named after [[Thomas Henry Havelock]]. In fact, both the Bateman and the Havelock functionfunctions were first introduced by Havelock in 1927,<ref>Havelock, T. H. (1927). The method of images in some problems of surface waves. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(771), 268-280.</ref> while investigating the surface elevation of the uniform stream past an immersed circular cylinder. The Havelock function is defined by

:<math>\displaystyle h_\nu(x) = \frac{2}{\pi}\int_0^{\pi/2}\sin(x\tan\theta-\nu\theta) \, d\theta .</math>