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Integral representation of Kelvin functions and their derivatives with respect to the order

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Integral representations of the Kelvin functions ber v x and bei v 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.

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Apelblat, A. Integral representation of Kelvin functions and their derivatives with respect to the order. Z. angew. Math. Phys. 42, 708–714 (1991).

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