Sur deux formules de Frobenius et Stickelberger et inversion de Lagrange

TL;DR

This paper extends classical formulas of Frobenius and Stickelberger related to elliptic functions by introducing a generalized bilinear form, providing new proofs and connections to Lagrange's product formula and Olver's theorem.

Contribution

It introduces a broad generalization of Leibniz's formula through a bilinear form, offering new proofs and extensions of fundamental elliptic function formulas.

Findings

Generalization of Leibniz formula via bilinear form

New proof of Frobenius and Stickelberger formulas

Connection to Lagrange product formula and Olver's theorem

Abstract

We give a proof and extension of two formulas of Frobenius and Stickelberger of Differential Calculus that they used in a fundamental paper concerning elliptic functions theory. Our main ingredient is the introduction of a bilinear form which is a vast generalization of Leibniz formula. This bilinear form is also connected to the Lagrange product formula. As a corollary, we give a different proof of a theorem of P.J. Olver.