elliptic integral
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An elliptic integral is a mathematical integral involving a function that is rational in its argument and the square root of a polynomial of the third or fourth degree. These integrals arose from attempts to calculate the length of an arc of an ellipse, hence their name.12
While these integrals cannot be explicitly evaluated using standard functions, their study led to significant advancements in mathematics. In the 19th century, mathematicians like Niels Henrik Abel and Carl Jacobi transformed the field by considering complex variables, leading to the development of elliptic functions. These functions possess properties analogous to trigonometric functions and became a foundational model for the study of functions of a complex variable.2
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- John Landen
…who made important contributions on elliptic integrals.
Read More…who made important contributions on elliptic integrals.
Read More - Adrien-Marie Legendre
…Legendre took up research on elliptic integrals. 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…
Read More…Legendre took up research on elliptic integrals. 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…
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