Abstract
Authors of different texts on physics and applied mathematics choose different definitions for the special functions. Some obtain series solutions to the differential equation and define the corresponding special function in terms of these series, others prefer to use the generating function as the defining relation, still others elect to start with a Rodrigues formula for the special function, and a few take an integral representation as a definition. It is interesting and instructive to see that these various ways of defining a given special function are all equivalent.
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© 1991 Springer Science+Business Media New York
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Seaborn, J.B. (1991). Alternate Forms for Special Functions. 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_9
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DOI: https://doi.org/10.1007/978-1-4757-5443-8_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3097-2
Online ISBN: 978-1-4757-5443-8
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