The Operational Calculus of Legendre Transforms

Some properties of generalized fractional integral with Lengendre functions kernel’s

“…Churchill introduced in [3] the Legendre transform of a function and developed its operational calculus. In [4] the authors introduced the associated Legendre transform,…”

The continous Legendre transform, its inverse transform, and applications

“…Tranter (15) and R.V. Churchill (7) examined in some detail the (discrete) Legendre transform, which is defined in terms of the Legendre polynomials Pk(X), kEP={0,1,2,...}, and discussed its applicability mainly to the solution of partial differential equations. The present authors dealt with applications of this transform to a variety of problems in approximation theory in (14), (4), (5).…”

Operational calculs for the continuous Legendre transform with applications

“…The discrete analog of the transform ill (1) has been studied by Churchill [2] and Churchill and Dolph [3]. The object of this paper is to develop an operational calculus for the transforin which is useful in solving paxtial differential equations whose underlying differential forln is given by D=xx (1-x)xx (2) Ill section 2 we present the background material needed in the sequel. In section 3, ve derive the operational calculus for (1) including a convolution theorem and a table of transforms of some functions.…”

“…PRELIMINARIES. We recall basic properties of the transform (Tf)(A) (see [1] (2). Fher, i satisfies tim relations P(1) P (1) lira.__ , (1+…”

“…The addition formula for the Legendre functions (see [4] [2] and Churchill and Dolph [3] for the discrete case.…”