# Special Functions in Applied Mathematics

Chapter

## Abstract

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.

## Keywords

Power Series Special Function Gamma Function Hypergeometric Function Resonant Cavity
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## References

- 1.For more detail see, for example, W. Kaplan,
*Advanced Calculus*, Addison-Wesley, Reading, MA, 1953.Google Scholar - 5.J.D. Jackson,
*Classical Electrodynamics*, Wiley, New York, 1962, p. 253.Google Scholar - 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 - 10.For example, see F. Reif,
*Fundamentals of Statistical and Thermal Physics*, McGraw-Hill, New York, 1965, p. 267.Google Scholar - 11.N.N. Lebedev,
*Special Functions and Their Applications*, Dover, New York, 1972, p. 1.zbMATHGoogle Scholar - 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