A table of Legendre-transformation pairs with methodologies for construction, authentication, and approximation of pairs

2022/08/09 by Kolt, Quinn T., Kilner, Steven J., Farnsworth, David L.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.05043

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.

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