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Expressions for the derivatives with respect to order of modified Besselfunctions evaluated at integer orders and certain integral representations ofassociated Legendre functions with modulus argument greater than unity are usedto compute derivatives of the associated Legendre functions with respect totheir parameters. For the associated Legendre functions of the first and secondkind, derivatives with respect to the degree are evaluated at odd-half-integerdegrees, for general complex orders, and derivatives with respect to the orderare evaluated at integer orders, for general complex degrees.

Derivatives with respect to the degree and order of associated Legendre functions for $|z|>1$ using modified Bessel functions