Submitted:
09 March 2018
Posted:
09 March 2018
You are already at the latest version
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.
Keywords:
q-calculus
; (p
; q)-calculus
; exponential functions
; trigonometric functions
; hyperbolic functions
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