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Hypergeometric functions
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  • Hypergeometric Orthogonal Polynomials and Their q-Analoguesby Roelof Koekoek; Peter A. Lesky; Rene F. Swarttouw

    Springer 2010; US$ 129.00

    The very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function.Replacing the differential equation by a second-order difference equation results in (discrete) orthogonal polynomial solutions with similar properties. Generalizations of these difference equations, in terms of Hahn's q-difference operator, lead to both continuous and discrete orthogonal polynomials with similar properties. For instance, they can be expressed in terms of (basic) hypergeometric functions.Based on Favard's theorem, the authors first classify all families... more...

  • Basic Hypergeometric Seriesby George Gasper; Mizan Rahman

    Cambridge University Press 2004; US$ 140.00

    Significant revision of classic reference in special functions. more...

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