Traité des fonctions elliptiques

work by Legendre

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July 16, 2026

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Adrien-Marie Legendre, a French mathematician, made significant contributions to the study of elliptic integrals in his work Traité des fonctions elliptiques (1825–37). He reduced these integrals to three standard forms, now known as Legendre's forms, and compiled tables of their values. These tools were crucial for solving problems in mechanics and dynamics. While Legendre's work was foundational, the field was revolutionized by the independent discoveries of Niels Henrik Abel and Carl Jacobi, who developed the theory of elliptic functions by considering complex variables.12

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Adrien-Marie Legendre
In his most important work, Traité des fonctions elliptiques (1825–37; “Treatise on Elliptic Functions”), he reduced elliptic integrals to three standard forms now known by his name. He also compiled tables of the values of his elliptic integrals and showed how they can be used to solve important problems in…
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In his most important work, Traité des fonctions elliptiques (1825–37; “Treatise on Elliptic Functions”), he reduced elliptic integrals to three standard forms now known by his name. He also compiled tables of the values of his elliptic integrals and showed how they can be used to solve important problems in…
Read More