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mathematical physics > special function > hypergeometric function > Bateman function

mathematical analysis > functional analysis > special function > hypergeometric function > Bateman function

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Bateman function

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

${\\displaystyle \\displaystyle k_{n}(x)={\ rac {2}{\\pi }}\\int _{0}^{\\pi /2}\\cos(x\ an \ heta -n\ heta )\\,d\ heta }$

Bateman discovered this function, when Theodore von Kármán asked for the solution of the following differential equation which appeared in the theory of turbulence

${\\displaystyle x{\ rac {d^{2}u}{dx^{2}}}=(x-n)u}$

and Bateman found this function as one of the solutions. Bateman denoted this function as "k" function in honor of Theodore von Kármán.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Bateman_function)

hypergeometric function

k-function

fonction de Bateman

francés

URI

http://data.loterre.fr/ark:/67375/PSR-GND317C1-S

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