On aq-generalization of circular and hyperbolic functions
- 12 June 1998
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 31 (23), 5281-5288
- https://doi.org/10.1088/0305-4470/31/23/011
Abstract
A generalization of the circular and hyperbolic functions is proposed, based on the Tsallis statistics and on a consistent generalization of the Euler formula. Some properties of the presently proposed q-trigonometry are then investigated. The generalized functions are exact solutions of a nonlinear oscillator. Original circular and hyperbolic relations are recovered as the limiting case.Keywords
This publication has 43 references indexed in Scilit:
- On the Fourier - Gauss transforms of someq-exponential andq-trigonometric functionsJournal of Physics A: General Physics, 1996
- On a one-parameter family ofq-exponential functionsJournal of Physics A: General Physics, 1996
- On the coherent states for theq-Hermite polynomials and related Fourier transformationJournal of Physics A: General Physics, 1996
- More on the q-oscillator algebra and q-orthogonal polynomialsJournal of Physics A: General Physics, 1995
- q-exponential and q-gamma functions. I. q-exponential functionsa)Journal of Mathematical Physics, 1995
- Automorphisms of the q-oscillator algebra and basic orthogonal polynomialsPhysics Letters A, 1993
- Quantum Algebras and q-Special FunctionsAnnals of Physics, 1993
- q-Orthogonal polynomials and the oscillator quantum groupLetters in Mathematical Physics, 1991
- On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)qJournal of Physics A: General Physics, 1989
- The quantum group SUq(2) and a q-analogue of the boson operatorsJournal of Physics A: General Physics, 1989