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Hypergeometric Orthogonal Polynomials and Their q-Analogues

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...

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Autori principali: Koekoek, Roelof. (Autore, http://id.loc.gov/vocabulary/relators/aut), Lesky, Peter A. (http://id.loc.gov/vocabulary/relators/aut), Swarttouw, René F. (http://id.loc.gov/vocabulary/relators/aut)
Ente Autore: SpringerLink (Online service)
Natura: Elettronico eBook
Lingua:English
Pubblicazione: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2010.
Edizione:1st ed. 2010.
Serie:Springer Monographs in Mathematics,
Soggetti:
Mathematical analysis.
Analysis (Mathematics).
Special functions.
Analysis.
Special Functions.
Accesso online:https://doi.org/10.1007/978-3-642-05014-5
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Sommario:
  • Definitions and Miscellaneous Formulas
  • Classical orthogonal polynomials
  • Orthogonal Polynomial Solutions of Differential Equations
  • Orthogonal Polynomial Solutions of Real Difference Equations
  • Orthogonal Polynomial Solutions of Complex Difference Equations
  • Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations
  • Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations
  • Hypergeometric Orthogonal Polynomials
  • Polynomial Solutions of Eigenvalue Problems
  • Classical q-orthogonal polynomials
  • Orthogonal Polynomial Solutions of q-Difference Equations
  • Orthogonal Polynomial Solutions in q?x of q-Difference Equations
  • Orthogonal Polynomial Solutions in q?x+uqx of Real.

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