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Integral representation of Kelvin functions and their derivatives with respect to the order. (English) Zbl 0741.33002
Integral representations of the Kelvin functions \(\hbox{ber}_ \nu x\) and \(\hbox{bei}_ \nu x\) and their derivatives with respect to the order are considered. Using the Laplace transform technique the derivatives are expressed in terms of finite integrals. The Kelvin functions \(\hbox{ber}_{n+1/2}x\) and \(\hbox{bei}_{n+1/2}x\) can be presented in a closed form.

33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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