A New Generating Function for Hermite Polynomials
This paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of th...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/9075713 |
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| _version_ | 1849718006470410240 |
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| author | Manouchehr Amiri |
| author_facet | Manouchehr Amiri |
| author_sort | Manouchehr Amiri |
| collection | DOAJ |
| description | This paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of the generating function. New versions of the generating functions for the two-variable Hermite polynomials have been presented. |
| format | Article |
| id | doaj-art-83c13a7adf4e4fab84947b6fbb63d5e6 |
| institution | DOAJ |
| issn | 1687-0425 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-83c13a7adf4e4fab84947b6fbb63d5e62025-08-20T03:12:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/9075713A New Generating Function for Hermite PolynomialsManouchehr Amiri0Independent ResearcherThis paper presents a new generating function of the form gx,t=∑n=0∞tnHnex for Hermite polynomials and reveals its connection with the incomplete gamma function. Recurrence relations of Hermite polynomials and another version of its contour integral representation are derived from this version of the generating function. New versions of the generating functions for the two-variable Hermite polynomials have been presented.http://dx.doi.org/10.1155/ijmm/9075713 |
| spellingShingle | Manouchehr Amiri A New Generating Function for Hermite Polynomials International Journal of Mathematics and Mathematical Sciences |
| title | A New Generating Function for Hermite Polynomials |
| title_full | A New Generating Function for Hermite Polynomials |
| title_fullStr | A New Generating Function for Hermite Polynomials |
| title_full_unstemmed | A New Generating Function for Hermite Polynomials |
| title_short | A New Generating Function for Hermite Polynomials |
| title_sort | new generating function for hermite polynomials |
| url | http://dx.doi.org/10.1155/ijmm/9075713 |
| work_keys_str_mv | AT manouchehramiri anewgeneratingfunctionforhermitepolynomials AT manouchehramiri newgeneratingfunctionforhermitepolynomials |