Improved q-exponential and q-trigonometric functions

2010/06/29 by Jan L. Cieśliński, Cieśliński, Jan L.
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA) #math.CA #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.1006.5652

9 pages

arxiv created 2010/06/29 · arxiv updated 2010/11/04

Abstract

We propose a new definition of the q-exponential function. Our q-exponential function maps the imaginary axis into the unit circle and the resulting q-trigonometric functions are bounded and satisfy the Pythagorean identity.

Related

• q-Calculus Revisited
• On certain q-trigonometric identities
• On A Relation Between q-Exponential And θ-Function
• Jackson's q-exponential as the exponential of a series
• Hypergeometric Functions II (q-analogues)