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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 ${\text{ber}}_{\nu }x$ and ${\text{bei}}_{\nu }x$ 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 ${\text{ber}}_{n+1/2}x$ and ${\text{bei}}_{n+1/2}x$ can be presented in a closed form.
##### MSC:
 33C10 Bessel and Airy functions, cylinder functions, ${}_{0}{F}_{1}$
Kelvin functions
##### References:
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