A note on the order derivatives of Kelvin functions

Abstract

We calculate the derivative of the berν , beiν , kerν , and keiν functions with respect to the order ν in closed-form for ν ∈ R. Unlike the expressions found in the literature for order derivatives of the berν and beiν functions, we provide much more simple expressions that are also applicable for negative integral order. The expressions for the order derivatives of the kerν and keiν functions seem to be novel. Also, as a by-product, we calculate some new integrals involving the berν and beiν functions in closed-form. Finally, we include a simple derivation of some integral representations of the ber and bei functions.