The continous Legendre transform, its inverse transform, and applications
The continous Legendre transform, its inverse transform, and applications
This paper is concerned with the continuous Legendre transform, derived from the classical discrete Legendre transform by replacing the Legendre polynomial P k ( x ) by the function P λ ( x ) with λ real. Another approach to T.M. MacRobert′s inversion formula is found; for this purpose an …