Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family
The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of polynomials will be established. In addition, these...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/4/211 |
| _version_ | 1797446359981228032 |
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| author | Tabinda Nahid Junesang Choi |
| author_facet | Tabinda Nahid Junesang Choi |
| author_sort | Tabinda Nahid |
| collection | DOAJ |
| description | The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of polynomials will be established. In addition, these specific matrix polynomials are interpreted in terms of quasi-monomiality. The extended versions of the Gould-Hopper-Laguerre-Sheffer matrix polynomials are introduced, and their characteristics are explored using the integral transform. Further, examples of how these results apply to specific members of the matrix polynomial family are shown. |
| first_indexed | 2024-03-09T13:39:25Z |
| format | Article |
| id | doaj.art-7da3e21919cb4ea1ac8eaf6113e76486 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T13:39:25Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-7da3e21919cb4ea1ac8eaf6113e764862023-11-30T21:08:44ZengMDPI AGFractal and Fractional2504-31102022-04-016421110.3390/fractalfract6040211Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer FamilyTabinda Nahid0Junesang Choi1Department of Mathematics, Aligarh Muslim University, Aligarh 202001, IndiaDepartment of Mathematics, Dongguk University, Gyeongju 38066, KoreaThe main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of polynomials will be established. In addition, these specific matrix polynomials are interpreted in terms of quasi-monomiality. The extended versions of the Gould-Hopper-Laguerre-Sheffer matrix polynomials are introduced, and their characteristics are explored using the integral transform. Further, examples of how these results apply to specific members of the matrix polynomial family are shown.https://www.mdpi.com/2504-3110/6/4/211Gould-Hopper-Laguerre-Sheffer matrix polynomialsquasi-monomialityumbral calculusfractional calculusEuler’s integral of gamma functionsbeta function |
| spellingShingle | Tabinda Nahid Junesang Choi Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family Fractal and Fractional Gould-Hopper-Laguerre-Sheffer matrix polynomials quasi-monomiality umbral calculus fractional calculus Euler’s integral of gamma functions beta function |
| title | Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family |
| title_full | Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family |
| title_fullStr | Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family |
| title_full_unstemmed | Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family |
| title_short | Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family |
| title_sort | certain hybrid matrix polynomials related to the laguerre sheffer family |
| topic | Gould-Hopper-Laguerre-Sheffer matrix polynomials quasi-monomiality umbral calculus fractional calculus Euler’s integral of gamma functions beta function |
| url | https://www.mdpi.com/2504-3110/6/4/211 |
| work_keys_str_mv | AT tabindanahid certainhybridmatrixpolynomialsrelatedtothelaguerreshefferfamily AT junesangchoi certainhybridmatrixpolynomialsrelatedtothelaguerreshefferfamily |