Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The $ Ateb(h)$-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.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/143948
Article copyright: © Copyright 1963 American Mathematical Society


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