LAUSR

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