q-Calculus Revisited
General Mathematics
2021-06-09 v1
Authors:
Si Hyung Joo
Abstract
In this study, a new representation is obtained for \emph{q}-calculus, as proposed by Borges [Phyica A 340 (2004) 95], and a new dual \emph{q}-integral is suggested.
Keywords
Cite
@article{arxiv.2106.03855,
title = {q-Calculus Revisited},
author = {Si Hyung Joo},
journal= {arXiv preprint arXiv:2106.03855},
year = {2021}
}
Related papers
View all related →
Classical Analysis and ODEs · Mathematics
Can Umbral and $q$-calculus be merged?
G. Dattoli, B. Germano, K. Górska, M. R. Martinelli
2019-09-04
General Mathematics · Mathematics
On a New Type $pq$-Calculus
İlker Gençtürk
2019-11-27
Number Theory · Mathematics
A New Approach to Multivariate q-Euler polynomials by using Umbral calculus
Serkan Araci, Xiangxing Kong, Mehmet Acikgoz, Erdoğan Şen
2014-02-04
Classical Analysis and ODEs · Mathematics
New proofs of theorems on q-orthogonal functions
Dandan Chen, Zhiguo Liu
2024-08-09
Classical Analysis and ODEs · Mathematics
An extension of basic Humbert hypergeometric functions {\Phi}1, {\Phi}2 and {\Phi}3
Ayman Shehata
2025-02-11
q-alg · Mathematics
The $q$-calculus for generic $q$ and $q$ a root of unity
R. S. Dunne, A. J. Macfarlane, J. A. de Azcárraga, J. C. Pérez Bueno
2009-10-30
Classical Analysis and ODEs · Mathematics
New approach to generalized Mittag-Leffler function via quantum calculus
Raghib Nadeem, Mohd. Saif, Talha Usman, Abdul Hakim Khan
2019-01-18
Complex Variables · Mathematics
Harmonic univalent functions defined by q-calculus operators
Jay M. Jahangiri
2018-06-25
Number Theory · Mathematics
A note on q-Volkenborn integration
T. Kim
2007-05-23
Number Theory · Mathematics
Identities for the q-harmonic numbers and q-binomial coefficients
Ce Xu
2017-10-24
Complex Variables · Mathematics
On integral representations of $q$-difference operators and their applications
Antonio Cáceres, Alberto Lastra, Sławomir Michalik, Maria Suwińska
2026-03-27
Quantum Algebra · Mathematics
On the fundamental theorem of $(p,q)$-calculus and some $(p,q)$-Taylor formulas
P. Njionou Sadjang
2013-09-17
High Energy Physics - Theory · Physics
Comment on "Dual path integral representation for finite temperature quantum field theory"
P. O. Kazinski
2008-09-11
High Energy Physics - Theory · Physics
Q-Deformed Path Integral
M. Chaichian, A. P. Demichev
2009-10-22
Functional Analysis · Mathematics
Generalized $q$-Fock spaces and structural identities
Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider
2023-09-11
Classical Analysis and ODEs · Mathematics
On a new $q$-analogue of Appell polynomials
P. Njionou Sadjang
2018-01-29
Number Theory · Mathematics
New representations for $\sigma(q)$ via reciprocity theorems
Koustav Banerjee, Atul Dixit
2016-07-20
High Energy Physics - Theory · Physics
Representation of Quantum Algebras and q-Special Functions
R. Floreanini, L. Vinet
2008-02-03
Number Theory · Mathematics
A $(p,q)$-Analogue of Poly-Euler Polynomials and Some Related Polynomials
Takao Komatsu, José L. Ramírez, Víctor F. Sirvent
2016-04-14
Mathematical Physics · Physics
On a conjecture about Dirac's delta representation using q-exponentials
A. Chevreuil, A. Plastino, C. Vignat
2015-05-19
General Mathematics · Mathematics
Opial's inequality in $q$-Calculus revisited
Tatjana Z. Mirkovic, Slobodan B. Trickovic, Miomir S. Stankovic
2024-04-10
Quantum Algebra · Mathematics
Quantum matrix ball: differential and integral calculi
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
2007-05-23
Functional Analysis · Mathematics
Tsallis' q-analysis, new scales of interpolating spaces and q-rational functions
Daniel Alpay, Paula Cerejeiras, Uwe Kaehler
2025-05-22
Combinatorics · Mathematics
A $q$-deformation of enriched $P$-partitions (extended abstract)
Darij Grinberg, Ekaterina A. Vassilieva
2023-07-19
General Physics · Physics
Common aspects of q-deformed Lie algebras and fractional calculus
Richard Herrmann
2014-11-21