A STUDY ON SOME NEW RESULTS ARISING FROM (p, q)-CALCULUS - Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan; Aracı, Serkan (INST APPLIED MATHEMATICS, 2020)
This paper includes some new investigations and results for post quantum calculus, denoted by (p, q)-calculus. A chain rule for (p, q)-derivative is given. Also, a new (p, q)-analogue of the exponential function is introduced and its properties including the addition property for (p, q)-exponential functions are investigated. Several useful results involving (p, q)binomial co-efficients and (p, q)-antiderivative are discovered. At the final part of this paper, (p, q)-analogue of some elementary functions including trigonometric functions and hyperbolic functions are considered and some properties and relations among them are analyzed extensively.
Keywords: q-Calculus; (p,q)-Calculus; exponential functions; trigonometric functions; hyperbolic functions