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  • © 1988

Special Functions of Mathematical Physics

A Unified Introduction with Applications

Birkhäuser

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xviii
  2. Foundations of the Theory of Special Functions

    • Arnold F. Nikiforov, Vasilii B. Uvarov
    Pages 1-19
  3. The Classical Orthogonal Polynomials

    • Arnold F. Nikiforov, Vasilii B. Uvarov
    Pages 21-200
  4. Bessel Functions

    • Arnold F. Nikiforov, Vasilii B. Uvarov
    Pages 201-251
  5. Hypergeometric functions

    • Arnold F. Nikiforov, Vasilii B. Uvarov
    Pages 253-294
  6. Back Matter

    Pages 369-427

About this book

With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan­ tum mechanics. We have not attempted to provide the most extensive collec­ tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro­ vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or­ thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics.

Keywords

  • Bessel function
  • gamma function
  • Hypergeometric function
  • integral
  • Mathematica
  • mathematical physics
  • mechanics
  • numerical analysis
  • orthogonal polynomials
  • quantum mechanics
  • solution
  • special function

Authors and Affiliations

  • M.V. Keldish Institute of Applied Mathematics of the Academy of Sciences of the USSR, Moscow, USSR

    Arnold F. Nikiforov, Vasilii B. Uvarov

Bibliographic Information

  • Book Title: Special Functions of Mathematical Physics

  • Book Subtitle: A Unified Introduction with Applications

  • Authors: Arnold F. Nikiforov, Vasilii B. Uvarov

  • DOI: https://doi.org/10.1007/978-1-4757-1595-8

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1988

  • Softcover ISBN: 978-1-4757-1597-2

  • eBook ISBN: 978-1-4757-1595-8

  • Edition Number: 1

  • Number of Pages: XVIII, 427

  • Topics: Special Functions, Applications of Mathematics, Mathematical Methods in Physics

Buying options

eBook
USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-1-4757-1595-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 139.99
Price excludes VAT (USA)