n Parameter Differentiation for Integral Representations of Associated Legendre Functions

On Parameter Differentiation for Integral Representations of Associated Legendre Functions

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-halfinteger degrees, for general complex-orders, ...

Legendre-type integrands and convex integral functions

In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

Properties of multivalent functions associated with certain integral operator

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

The Study of Triple Integral Equations with Generalized Legendre Functions