$(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula

Authors

  • İlker Gençtürk Department of Mathematics, Kırıkkale University, Turkey

DOI:

https://doi.org/10.3842/umzh.v77i9.8966

Keywords:

(p,q)-analyticity, complex (p,q)-binomial, (p,q)-Taylor expansion

Abstract

UDC 517.5

We introduce the notions of $(p,q)$-differential for complex discrete functions and $(p,q)$-complex differential operators in a sense of Pashaev. The $(p,q)$-analog of the $q$-binomial formula is presented and the $(p,q)$-Taylor expansion is constructed for $(p,q)$-analytic functions. These results provide a generalized framework for $(p,q)$-calculus, contributing to its applications in mathematical analysis and related fields.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 9, 2025.

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Published

06.11.2025

Issue

Vol. 77 No. 9 (2025)

Section

Research articles

License

Copyright (c) 2025 İlker Gençtürk

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Gençtürk İlker. “$(p,q)$-Analytic Functions and a Complex $(p,q)$-Binomial Formula”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 9, Nov. 2025, p. 593, https://doi.org/10.3842/umzh.v77i9.8966.