Integral representation of Kelvin functions and their derivatives with respect to the order (Q1180662)

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.