An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials
In recent years, the generating function of mixed-type special polynomials has received growing interest in several fields of applied sciences and physics. This article intends to study a new class of polynomials, called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/Math...
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2029 |
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| author | Shahid Ahmad Wani Sarfaraj Shaikh Parvez Alam Shahid Tamboli Mohra Zayed Javid G. Dar Mohammad Younus Bhat |
| author_facet | Shahid Ahmad Wani Sarfaraj Shaikh Parvez Alam Shahid Tamboli Mohra Zayed Javid G. Dar Mohammad Younus Bhat |
| author_sort | Shahid Ahmad Wani |
| collection | DOAJ |
| description | In recent years, the generating function of mixed-type special polynomials has received growing interest in several fields of applied sciences and physics. This article intends to study a new class of polynomials, called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Frobenius–Genocchi–Appell polynomials. The generating function of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Frobenius–Genocchi–Appell polynomials is constructed and some of their fundamental properties are studied. By making use of this generating function, we investigate some novel and interesting results, such as recurrence relations, explicit representations, and implicit formulas for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Frobenius–Genocchi–Appell polynomials. The quasi-monomiality and determinant form for these polynomials are established. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Genocchi–Appell polynomials are explored as a special case and several results for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Genocchi–Appell polynomials are also obtained. |
| first_indexed | 2024-03-11T04:13:39Z |
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| id | doaj.art-e29ee6e1e86f4e74bdee940a70124d82 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:13:39Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-e29ee6e1e86f4e74bdee940a70124d822023-11-17T23:19:04ZengMDPI AGMathematics2227-73902023-04-01119202910.3390/math11092029An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell PolynomialsShahid Ahmad Wani0Sarfaraj Shaikh1Parvez Alam2Shahid Tamboli3Mohra Zayed4Javid G. Dar5Mohammad Younus Bhat6Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, IndiaDepartment Mechanical Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 600127, IndiaDepartment Mechanical Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, IndiaMathematics Department, College of Science, King Khalid University, Abha 61421, Saudi ArabiaDepartment of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, IndiaDepartment of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, IndiaIn recent years, the generating function of mixed-type special polynomials has received growing interest in several fields of applied sciences and physics. This article intends to study a new class of polynomials, called the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Frobenius–Genocchi–Appell polynomials. The generating function of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Frobenius–Genocchi–Appell polynomials is constructed and some of their fundamental properties are studied. By making use of this generating function, we investigate some novel and interesting results, such as recurrence relations, explicit representations, and implicit formulas for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Frobenius–Genocchi–Appell polynomials. The quasi-monomiality and determinant form for these polynomials are established. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Genocchi–Appell polynomials are explored as a special case and several results for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Δ</mo><mi>h</mi></msub></semantics></math></inline-formula>-Genocchi–Appell polynomials are also obtained.https://www.mdpi.com/2227-7390/11/9/2029Frobenius–Genocchi polynomialsΔ<i><sub>h</sub></i>–Appell polynomialsquasi-monomialitydeterminant form |
| spellingShingle | Shahid Ahmad Wani Sarfaraj Shaikh Parvez Alam Shahid Tamboli Mohra Zayed Javid G. Dar Mohammad Younus Bhat An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials Mathematics Frobenius–Genocchi polynomials Δ<i><sub>h</sub></i>–Appell polynomials quasi-monomiality determinant form |
| title | An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials |
| title_full | An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials |
| title_fullStr | An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials |
| title_full_unstemmed | An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials |
| title_short | An Algebraic Approach to the Δ<i><sub>h</sub></i>-Frobenius–Genocchi–Appell Polynomials |
| title_sort | algebraic approach to the δ i sub h sub i frobenius genocchi appell polynomials |
| topic | Frobenius–Genocchi polynomials Δ<i><sub>h</sub></i>–Appell polynomials quasi-monomiality determinant form |
| url | https://www.mdpi.com/2227-7390/11/9/2029 |
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