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Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)

Vadim Schechtman (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.

Pseudo Laguerre and pseudo Hermite polynomials

Giuseppe Dattoli (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We start from pseudo hyperbolic and trigonometric functions to introduce pseudo Laguerre and Hermite polynomials. We discuss the link with families of Bessel functions and analyze all the associated problems from a unifying point of view, employing operational tools.

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