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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 ber ν x and bei ν 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 ber n+1/2 x and bei n+1/2 x can be presented in a closed form.
33C10Bessel and Airy functions, cylinder functions, 0 F 1
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