On the fundamental theorem of $(p,q)$-calculus and some $(p,q)$-Taylor formulas

Abstract

In this paper, the $(p,q)$-derivative and the $(p,q)$-integration are investigated. Two suitable polynomials bases for the $(p,q)$-derivative are provided and various properties of these bases are given. As application, two $(p,q)$-Taylor formulas for polynomials are given, the fundamental theorem of $(p,q)$-calculus is included and the formula of $(p,q)$-integration by part is proved.

15 pages, research article

References in corpus (2)

• Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series
• Quantum deformed algebras : Coherent states and special functions

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