Preprint Article Version 1 This version is not peer-reviewed

A Study on Some New Results Arising from (p,q)-Calculus

Version 1 : Received: 9 March 2018 / Approved: 9 March 2018 / Online: 9 March 2018 (14:49:59 CET)

How to cite: Duran, U.; Acikgoz, M.; Araci, S. A Study on Some New Results Arising from (p,q)-Calculus. Preprints 2018, 2018030072 (doi: 10.20944/preprints201803.0072.v1). Duran, U.; Acikgoz, M.; Araci, S. A Study on Some New Results Arising from (p,q)-Calculus. Preprints 2018, 2018030072 (doi: 10.20944/preprints201803.0072.v1).

Abstract

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 developed. Also, a new (p,q)-analogue of the exponential function is introduced and some its properties including the addition property for (p,q)-exponential functions are investigated. Several useful results involving (p,q)-binomial coefficients 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.

Subject Areas

q-calculus; (p,q)-calculus; exponential functions; trigonometric functions; hyperbolic functions

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