Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials
This manuscript introduces the family of Gould–Hopper–Lambda polynomials and establishes their quasi-monomial properties through the umbral method. This approach serves as a powerful mechanism to analyze the characteristic of multi-variable special polynomials. Several summation formulas for these p...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Maryam Salem Alatawi |
| author_facet | Maryam Salem Alatawi |
| author_sort | Maryam Salem Alatawi |
| collection | DOAJ |
| description | This manuscript introduces the family of Gould–Hopper–Lambda polynomials and establishes their quasi-monomial properties through the umbral method. This approach serves as a powerful mechanism to analyze the characteristic of multi-variable special polynomials. Several summation formulas for these polynomials are explored, and their operational identities are obtained using partial differential equations. The corresponding results for Hermite–Lambda polynomials are also obtained. In addition, a conclusion is given. |
| format | Article |
| id | doaj-art-58561847b98143f99fd91a15d6b376db |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-58561847b98143f99fd91a15d6b376db2025-01-24T13:39:40ZengMDPI AGMathematics2227-73902025-01-0113218610.3390/math13020186Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda PolynomialsMaryam Salem Alatawi0Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi ArabiaThis manuscript introduces the family of Gould–Hopper–Lambda polynomials and establishes their quasi-monomial properties through the umbral method. This approach serves as a powerful mechanism to analyze the characteristic of multi-variable special polynomials. Several summation formulas for these polynomials are explored, and their operational identities are obtained using partial differential equations. The corresponding results for Hermite–Lambda polynomials are also obtained. In addition, a conclusion is given.https://www.mdpi.com/2227-7390/13/2/186Lambda polynomialsumbral methoddifferential equationsummation formulasoperational identities |
| spellingShingle | Maryam Salem Alatawi Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials Mathematics Lambda polynomials umbral method differential equation summation formulas operational identities |
| title | Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials |
| title_full | Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials |
| title_fullStr | Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials |
| title_full_unstemmed | Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials |
| title_short | Certain Summation and Operational Formulas Involving Gould–Hopper–Lambda Polynomials |
| title_sort | certain summation and operational formulas involving gould hopper lambda polynomials |
| topic | Lambda polynomials umbral method differential equation summation formulas operational identities |
| url | https://www.mdpi.com/2227-7390/13/2/186 |
| work_keys_str_mv | AT maryamsalemalatawi certainsummationandoperationalformulasinvolvinggouldhopperlambdapolynomials |