HERMITE, CHARLES. - INTRODUCING "HERMITE-FUNCTIONS" - "HERMITE POLYNOMIALS"

Sur un nouveasu développement en série des fonctions. (2 Parts).

(Paris, Mallet-Bachelier), 1864. 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences", Tome 58, No 2 and No. 6. Pp. (93-) 140 a. pp. (261-) 296. (2 entire issues offered). hermite's paper: pp. 93-100 a. pp. 266-273.

First appearance of a famous paper in which Hermite introduced "Hermite-functions", solving differential equations over infinite intervals.

"The Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; in numerical analysis as Gaussian quadrature; in finite element methods as Shape Functions for beams; and in physics, where they give rise to the eigenstates of the quantum harmonic oscillator. They are also used in systems theory in connection with nonlinear operations on Gaussian noise. They are named after Charles Hermite (1864) (the paper offered) although they were studied earlier by Laplace (1810) and Chebyshev (1859)."(Wikipedia).

Order-nr.: 48185