The π΄π‘ππ(β)-functions and their properties
Open Access
- 1 January 1963
- journal article
- Published byΒ American Mathematical Society (AMS)Β inΒ Quarterly of Applied Mathematics
- Vol.Β 21Β (1), 37-47
- https://doi.org/10.1090/qam/143948
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.Keywords
This publication has 1 reference indexed in Scilit:
- Nichtlineare MechanikPublished by Springer Nature ,1958