$(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula
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. Thes...
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| Дата: | 2026 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8966 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513347076620288 |
|---|---|
| author | Gençtürk, İlker Gençtürk, İlker |
| author_facet | Gençtürk, İlker Gençtürk, İlker |
| author_sort | Gençtürk, İlker |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:33:57Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v77i9.8966 |
| first_indexed | 2026-03-24T03:43:14Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8966 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:43:14Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-89662026-03-21T13:33:57Z $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula Gençtürk, İlker Gençtürk, İlker (p,q)-analyticity complex (p,q)-binomial (p,q)-Taylor expansion 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. УДК 517.5 $(p,q)$-Aналітичні функції та комплексна $(p,q)$-біноміальна формула Введено поняття $(p,q)$-диференціала для комплексних дискретних функцій і $(p,q)$-комплексні диференціальні оператори в сенсі Пашаєва. Наведено $(p,q)$-аналог $q$-біноміальної формули та отримано $(p,q)$-розклад Тейлора для $(p,q)$-аналітичних функцій. Ці результати забезпечують узагальнену основу $(p,q)$-числення та сприяють його застосуванням у математичному аналізі й суміжних галузях. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8966 10.3842/umzh.v77i9.8966 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 9 (2025); 593 Український математичний журнал; Том 77 № 9 (2025); 593 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8966/10564 Copyright (c) 2025 İlker Gençtürk |
| spellingShingle | Gençtürk, İlker Gençtürk, İlker $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title | $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title_alt | $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title_full | $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title_fullStr | $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title_full_unstemmed | $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title_short | $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula |
| title_sort | $(p,q)$-analytic functions and a complex $(p,q)$-binomial formula |
| topic_facet | (p,q)-analyticity complex (p,q)-binomial (p,q)-Taylor expansion |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8966 |
| work_keys_str_mv | AT gencturkilker pqanalyticfunctionsandacomplexpqbinomialformula AT gencturkilker pqanalyticfunctionsandacomplexpqbinomialformula |