On the Fundamental Theorem of (p,q)-Calculus and Some (p,q)-Taylor Formulas

In this paper, the ( p ,  q )-derivative and the ( p ,  q )-integration are investigated. Two suitable polynomial 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 fundamenta...

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Bibliographic Details
Published in:Resultate der Mathematik Vol. 73; no. 1
Main Author: Njionou Sadjang, P.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2018
Subjects:
Mathematics
Mathematics and Statistics
30E10
fundamental theorem
30K05
Derivative
integration
30E05
33D60
Taylor formula
integration by part
ISSN:1422-6383, 1420-9012
Online Access:Get full text
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Summary:In this paper, the ( p ,  q )-derivative and the ( p ,  q )-integration are investigated. Two suitable polynomial 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.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-018-0783-z