## 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.

### MSC:

 33C10 Bessel and Airy functions, cylinder functions, $${}_0F_1$$

Kelvin functions
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### References:

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