Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters
UDC 517.584, 511.176 In the theory of orthogonal polynomials, extending classical polynomial families to multivariate and deformed settings often leads to rich and challenging generalizations. Motivated by recent developments in Fibonacci calculus and Bessel polynomial theory, this paper introduces...
Saved in:
| Date: | 2026 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9584 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1871646573919731712 |
|---|---|
| author | Riyasat, Mumtaz Riyasat, Mumtaz |
| author_facet | Riyasat, Mumtaz Riyasat, Mumtaz |
| author_institution_txt_mv | [
{
"author": "Mumtaz Riyasat",
"institution": "Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, India"
}
] |
| author_sort | Riyasat, Mumtaz |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:12Z |
| description | UDC 517.584, 511.176
In the theory of orthogonal polynomials, extending classical polynomial families to multivariate and deformed settings often leads to rich and challenging generalizations. Motivated by recent developments in Fibonacci calculus and Bessel polynomial theory, this paper introduces the $F$-Bessel (Fibonacci–Bessel) polynomials, the reverse $F$-Bessel polynomials, and their two-dimensional counterparts, the 2D $F$-Bessel polynomials. Several fundamental properties of these polynomial families are established, including generating functions, identities, differential recurrence relations, and determinant representations. The reverse $F$-Bessel polynomials are further employed to construct Fibonacci analogues of classical Bessel filters. Pole distributions for the third-, fourth-, fifth-, and sixth-order $F$-Bessel filters are analyzed, while the gain, phase, phase delay, and group delay characteristics of the third-order filter are numerically investigated and compared with those of the corresponding classical Bessel filter. The results demonstrate that the proposed $F$-Bessel filters preserve the desirable features of classical Bessel filters while exhibiting several enhanced performance characteristics. |
| doi_str_mv | 10.3842/umzh.v78i7-8.9584 |
| first_indexed | 2026-07-25T01:01:06Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9584 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:01:06Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-95842026-07-24T15:24:12Z Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters Riyasat, Mumtaz Riyasat, Mumtaz $F$-Bessel polynomials, Reverse $F$-Bessel polynomials, Fibonomial coefficient, 2D $F$-Bessel polynomials, $F$-Bessel Filter 11B83, 15A15, 33-04, 33F05, 33E99 UDC 517.584, 511.176 In the theory of orthogonal polynomials, extending classical polynomial families to multivariate and deformed settings often leads to rich and challenging generalizations. Motivated by recent developments in Fibonacci calculus and Bessel polynomial theory, this paper introduces the $F$-Bessel (Fibonacci–Bessel) polynomials, the reverse $F$-Bessel polynomials, and their two-dimensional counterparts, the 2D $F$-Bessel polynomials. Several fundamental properties of these polynomial families are established, including generating functions, identities, differential recurrence relations, and determinant representations. The reverse $F$-Bessel polynomials are further employed to construct Fibonacci analogues of classical Bessel filters. Pole distributions for the third-, fourth-, fifth-, and sixth-order $F$-Bessel filters are analyzed, while the gain, phase, phase delay, and group delay characteristics of the third-order filter are numerically investigated and compared with those of the corresponding classical Bessel filter. The results demonstrate that the proposed $F$-Bessel filters preserve the desirable features of classical Bessel filters while exhibiting several enhanced performance characteristics. УДК 517.584, 511.176 Узагальнення Фібоначчі поліномів Бесселя та їхнє застосування до аналогів Фібоначчі фільтрів Бесселя У теорії ортогональних поліномів розширення класичних сімей поліномів на багатовимірні та деформовані випадки часто приводить до змістовних і нетривіальних узагальнень. На основі недавніх результатів у численні Фібоначчі та теорії поліномів Бесселя введено $F$-поліноми Бесселя (поліноми Фібоначчі–Бесселя), обернені $F$-поліноми Бесселя та їхні двовимірні аналоги – двовимірні $F$-поліноми Бесселя. Встановлено низку фундаментальних властивостей цих сімей поліномів, зокрема отримано твірні функції, тотожності, диференціально-рекурентні співвідношення та визначникові подання. Обернені $F$-поліноми Бесселя використано для побудови аналогів Фібоначчі класичних фільтрів Бесселя. Проаналізовано розподіл полюсів $F$-фільтрів Бесселя третього, четвертого, п'ятого та шостого порядків. Чисельно досліджено та порівняно з відповідними характеристиками класичного фільтра Бесселя характеристики підсилення, фази, фазової затримки та групової затримки $F$-фільтра Бесселя третього порядку. Показано, що запропоновані $F$-фільтри Бесселя зберігають бажані властивості класичних фільтрів Бесселя, водночас демонструючи низку покращених експлуатаційних характеристик. Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9584 10.3842/umzh.v78i7-8.9584 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 612–613 Український математичний журнал; Том 78 № 7-8 (2026); 612–613 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9584/10691 Copyright (c) 2026 Mumtaz Riyasat |
| spellingShingle | Riyasat, Mumtaz Riyasat, Mumtaz Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title | Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title_alt | Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title_full | Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title_fullStr | Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title_full_unstemmed | Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title_short | Fibonacci-based generalizations of Bessel polynomials and their applications to Fibonacci-analogue Bessel filters |
| title_sort | fibonacci-based generalizations of bessel polynomials and their applications to fibonacci-analogue bessel filters |
| topic_facet | $F$-Bessel polynomials Reverse $F$-Bessel polynomials Fibonomial coefficient 2D $F$-Bessel polynomials $F$-Bessel Filter 11B83 15A15 33-04 33F05 33E99 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9584 |
| work_keys_str_mv | AT riyasatmumtaz fibonaccibasedgeneralizationsofbesselpolynomialsandtheirapplicationstofibonaccianaloguebesselfilters AT riyasatmumtaz fibonaccibasedgeneralizationsofbesselpolynomialsandtheirapplicationstofibonaccianaloguebesselfilters |