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.
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References
For more detail see, for example, W. Kaplan, Advanced Calculus, Addison-Wesley, Reading, MA, 1953.
J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1962, p. 253.
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.
For example, see F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965, p. 267.
N.N. Lebedev, Special Functions and Their Applications, Dover, New York, 1972, p. 1.
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.
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© 1991 Springer Science+Business Media New York
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Seaborn, J.B. (1991). Special Functions in Applied Mathematics. In: Hypergeometric Functions and Their Applications. Texts in Applied Mathematics, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5443-8_1
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DOI: https://doi.org/10.1007/978-1-4757-5443-8_1
Publisher Name: Springer, New York, NY
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