Special Functions in Applied Mathematics

  • James B. Seaborn
Part of the Texts in Applied Mathematics book series (TAM, volume 8)


Certain mathematical functions occur often enough in fields like physics and engineering to warrant special consideration. They form a class of well-studied functions with an extensive literature and, appropriately enough, are collectively called special functions. These functions carry such names as Bessel functions, Laguerre functions, and the like. Most of the special functions encountered in such applications have a common root in their relation to the hypergeometric function. The purpose of this book is to establish this relationship and use it to obtain many of the interesting and important properties of the special functions met in applied mathematics.


Power Series Special Function Gamma Function Hypergeometric Function Resonant Cavity 
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  1. 1.
    For more detail see, for example, W. Kaplan, Advanced Calculus, Addison-Wesley, Reading, MA, 1953.Google Scholar
  2. 5.
    J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1962, p. 253.Google Scholar
  3. 8.
    Some authors refer to this procedure as the method of Frobenius. The term appears to have a more restricted meaning as used by H. Jeffreys and B.S. Jeffreys, Methods of Mathematical Physics,Cambridge University Press, Cambridge, 1956, p. 482.Google Scholar
  4. 10.
    For example, see F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965, p. 267.Google Scholar
  5. 11.
    N.N. Lebedev, Special Functions and Their Applications, Dover, New York, 1972, p. 1.zbMATHGoogle Scholar
  6. 13.
    In this book, we assume that it is permissible to interchange orders of integration in repeated integrals. For a further discussion, see E.C. Titchmarsh, The Theory of Functions, Oxford University Press, Oxford, 1939, p. 53.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • James B. Seaborn
    • 1
  1. 1.Department of PhysicsUniversity of RichmondUSA

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