Some formulas of L. Carlitz on Hermite polynomials
We have used the idea of ‘quasi inner product’ introduced by L. R. Bragg in 1986 to consider generating series ∑n=0∞Hn2(x)Hn2(y)tn22n(n!)2 studied by L. Carlitz in 1963. The pecularity of the series is that there is (n!)2 in the denominator, which has a striking deviation from the usuaI generating s...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000996 |
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| author | S. K. Chatterjea S. M. Eaqub Ali |
| author_facet | S. K. Chatterjea S. M. Eaqub Ali |
| author_sort | S. K. Chatterjea |
| collection | DOAJ |
| description | We have used the idea of ‘quasi inner product’ introduced by L. R.
Bragg in 1986 to consider generating series
∑n=0∞Hn2(x)Hn2(y)tn22n(n!)2
studied by L. Carlitz in 1963. The pecularity of the series is that there is (n!)2
in the denominator, which has a striking deviation from the usuaI generating series
containing n! in the denominator. Our generating function for the said generating
series is quite different from that of Carlitz, but somewhat analogous to generating
integrals derived by G. N. Watson (Higher Transcendental function Vol.III, P 271-272
for the case of Legendre, Gegenbauer and Jacobi polynomials. |
| format | Article |
| id | doaj-art-9e21e730602d426783a1c2d64ac84fa7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9e21e730602d426783a1c2d64ac84fa72025-02-03T01:29:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114473774010.1155/S0161171291000996Some formulas of L. Carlitz on Hermite polynomialsS. K. Chatterjea0S. M. Eaqub Ali1Department of Mathematics, University of Calcutta, Calcutta 700 019, IndiaDepartment of Mathematics, University of Calcutta, Calcutta 700 019, IndiaWe have used the idea of ‘quasi inner product’ introduced by L. R. Bragg in 1986 to consider generating series ∑n=0∞Hn2(x)Hn2(y)tn22n(n!)2 studied by L. Carlitz in 1963. The pecularity of the series is that there is (n!)2 in the denominator, which has a striking deviation from the usuaI generating series containing n! in the denominator. Our generating function for the said generating series is quite different from that of Carlitz, but somewhat analogous to generating integrals derived by G. N. Watson (Higher Transcendental function Vol.III, P 271-272 for the case of Legendre, Gegenbauer and Jacobi polynomials.http://dx.doi.org/10.1155/S0161171291000996Hermite polynomialsgenerating functionquasi inner product. |
| spellingShingle | S. K. Chatterjea S. M. Eaqub Ali Some formulas of L. Carlitz on Hermite polynomials International Journal of Mathematics and Mathematical Sciences Hermite polynomials generating function quasi inner product. |
| title | Some formulas of L. Carlitz on Hermite polynomials |
| title_full | Some formulas of L. Carlitz on Hermite polynomials |
| title_fullStr | Some formulas of L. Carlitz on Hermite polynomials |
| title_full_unstemmed | Some formulas of L. Carlitz on Hermite polynomials |
| title_short | Some formulas of L. Carlitz on Hermite polynomials |
| title_sort | some formulas of l carlitz on hermite polynomials |
| topic | Hermite polynomials generating function quasi inner product. |
| url | http://dx.doi.org/10.1155/S0161171291000996 |
| work_keys_str_mv | AT skchatterjea someformulasoflcarlitzonhermitepolynomials AT smeaqubali someformulasoflcarlitzonhermitepolynomials |