The -functions and their properties

Author:
R. M. Rosenberg

Journal:
Quart. Appl. Math. **21** (1963), 37-47

MSC:
Primary 33.15

DOI:
https://doi.org/10.1090/qam/143948

MathSciNet review:
143948

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Abstract: The *Ateb(h)*-functions are inversions of incomplete Beta-functions. They are the solutions of normal mode vibrations of certain nonlinear multi-degree-of-freedom systems just as the trigonometric functions yield the normal mode vibrations of the corresponding linear systems. Like elliptic functions, the *Ateb(h)*-functions depend on a parameter. The *Ateb*-functions reduce to trigonometric functions, and the *Atebh*-functions to hyperbolic functions when the parameter is 1. When the parameter is 2, the *Ateb*-functions become elliptic functions. A number of properties of the *Ateb(h)*-functions, such as identities, derivatives, integrals, differential equations satisfied by them, etc., are given.

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DOI:
https://doi.org/10.1090/qam/143948

Article copyright:
© Copyright 1963
American Mathematical Society