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A table of Legendre-transformation pairs with methodologies for construction, authentication, and approximation of pairs (2208.05043v1)
Published 9 Aug 2022 in math.CA
Abstract: An extensive table of pairs of functions linked by the Legendre transformation is presented. Many special functions and formulas that are used in the sciences are included in the pairs. Formulations are provided for finding the Legendre transformations of analytic functions and of polynomial approximations to other functions.