Appell
In mathematics, "Appell" commonly refers to mathematicians Paul Émile Appell and, more broadly, to mathematical objects and concepts named after him. These primarily relate to special functions and polynomial sequences.
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Paul Émile Appell (1855-1930): A French mathematician and engineer. He is known for his work in analysis, mechanics, and differential equations. He held professorships at the Sorbonne and was President of the French Academy of Sciences.
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Appell Polynomials: A sequence of polynomials {Pn(x)} such that the derivative of Pn(x) is equal to n times Pn-1(x). More formally, P'n(x) = nPn-1(x). They are generalized by the property that their generating function has a specific form. Important examples of Appell polynomial sequences include the Hermite polynomials, Bernoulli polynomials, and Euler polynomials. They are often studied in relation to umbral calculus.
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Appell Functions: A class of bivariate hypergeometric functions of two complex variables. These functions were first studied by Appell. They are denoted by F1, F2, F3, and F4. Each function is a double power series and satisfies certain systems of partial differential equations. They are generalizations of the Gaussian hypergeometric function to two variables. Appell functions appear in various areas of mathematical physics.
The term "Appell" might also, in less common instances, relate to other concepts contributed or studied by Appell during his career. However, the aforementioned items represent the most frequently encountered use of "Appell" within mathematical discourse.