Polynomial Expansions of Analytic Functions : Reihe: Moderne Funktionentheorie

This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of result...

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Main Authors: Boas, Ralph P.Jr, Buck, R.C. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1958, 1958
Edition:1st ed. 1958
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Introduction
  • § 1. Generalities
  • § 2. Representation formulas with a kernel
  • § 3. The method of kernel expansion
  • § 4. Lidstone series
  • § 5. A set of Laguerre polynomials
  • § 6. Generalized Appell polynomials
  • II. Representation of entire functions
  • § 7. General theory
  • § 8. Multiple expansions
  • § 9. Appell polynomials
  • § 10. Sheffer polynomials
  • § 11. More general polynomials
  • § 12. Polynomials not in generalized Appell form
  • III. Representation of functions that are regular at the origin
  • § 13. Integral representations
  • § 14. Brenke polynomials
  • § 15. More general polynomials
  • § 16. Polynomials generated by A(?) (1 - zg(?))-?
  • § 17. Special hypergeometric polynomials
  • § 18. Polynomials not in generalized Appell form
  • IV. Applications
  • § 19. Uniqueness theorems
  • § 20. Functional equations