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Hypergeometric functions. --- Functions, Hypergeometric --- Transcendental functions --- Hypergeometric series

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In its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather than Jacobi?' Accordingly, it is based on the idea of inverting integrals which arise in the theory of differential equations and, in particular, the differential equation that describes the motion of a simple pendulum. The later chapters present a more conventional approach to the Weierstrass functions and to elliptic integrals, and then the reader is introduced to the richly varied applications of the elliptic and related functions. Applications spanning arithmetic (solution of the general quintic, the functional equation of the Riemann zeta function), dynamics (orbits, Euler's equations, Green's functions), and also probability and statistics, are discussed.

Elliptic functions --- Elliptic functions. --- Transcendental functions. --- Functions, Transcendental --- Functions, Special --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic

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Cascade flow. --- Annular ducts. --- Annular flow. --- Eigenvalues. --- Eigenvectors. --- High frequencies. --- Transcendental functions. --- Uniform flow.

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Fonctions d'une variable complexe --- Fonctions transcendantes. --- Functions of complex variables. --- Transcendental functions --- Fonctions speciales

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#WBIB:dd.Lic.L.De Busschere --- Bessel functions --- Cylindrical harmonics --- Transcendental functions --- Bessel polynomials --- Harmonic analysis --- Harmonic functions --- Fonctions speciales --- Fonctions de bessel