Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials
Let Pn={p(x)∈ℝ[x]∣deg p(x)≤n} be an inner product space with the inner product 〈p(x),q(x)〉=∫0∞xαe-xp(x)q(x)dx, where p(x),q(x)∈Pn and α∈ℝ with α>-1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for Pn. From those properties, we derive s...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/957350 |
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| author | Taekyun Kim Dae San Kim |
| author_facet | Taekyun Kim Dae San Kim |
| author_sort | Taekyun Kim |
| collection | DOAJ |
| description | Let Pn={p(x)∈ℝ[x]∣deg p(x)≤n} be an inner product space with the inner product 〈p(x),q(x)〉=∫0∞xαe-xp(x)q(x)dx, where p(x),q(x)∈Pn and α∈ℝ with α>-1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for Pn. From those properties, we derive some interesting relations and identities of the extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials. |
| format | Article |
| id | doaj-art-d9314027a7e442509a7e30443e9bf462 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d9314027a7e442509a7e30443e9bf4622025-08-20T03:24:15ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/957350957350Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and PolynomialsTaekyun Kim0Dae San Kim1Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDepartment of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaLet Pn={p(x)∈ℝ[x]∣deg p(x)≤n} be an inner product space with the inner product 〈p(x),q(x)〉=∫0∞xαe-xp(x)q(x)dx, where p(x),q(x)∈Pn and α∈ℝ with α>-1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for Pn. From those properties, we derive some interesting relations and identities of the extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials.http://dx.doi.org/10.1155/2012/957350 |
| spellingShingle | Taekyun Kim Dae San Kim Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials Abstract and Applied Analysis |
| title | Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials |
| title_full | Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials |
| title_fullStr | Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials |
| title_full_unstemmed | Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials |
| title_short | Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials |
| title_sort | extended laguerre polynomials associated with hermite bernoulli and euler numbers and polynomials |
| url | http://dx.doi.org/10.1155/2012/957350 |
| work_keys_str_mv | AT taekyunkim extendedlaguerrepolynomialsassociatedwithhermitebernoulliandeulernumbersandpolynomials AT daesankim extendedlaguerrepolynomialsassociatedwithhermitebernoulliandeulernumbersandpolynomials |