Hermite Polynomials and their Applications Associated with Bernoulli and Euler Numbers
We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x)∈ℚ[x]∣deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. Then we show that {H0(x),H1(x),…,Hn(x)} is a good basis for the space Pn for o...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/974632 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549922233122816 |
|---|---|
| author | Dae San Kim Taekyun Kim Seog-Hoon Rim Sang Hun Lee |
| author_facet | Dae San Kim Taekyun Kim Seog-Hoon Rim Sang Hun Lee |
| author_sort | Dae San Kim |
| collection | DOAJ |
| description | We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x)∈ℚ[x]∣deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. Then we show that {H0(x),H1(x),…,Hn(x)} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications. |
| format | Article |
| id | doaj-art-3172dd683e6f441c872871e7009fa7b1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3172dd683e6f441c872871e7009fa7b12025-02-03T06:08:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/974632974632Hermite Polynomials and their Applications Associated with Bernoulli and Euler NumbersDae San Kim0Taekyun Kim1Seog-Hoon Rim2Sang Hun Lee3Department of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaDepartment of Mathematics Education, Kyungpook National University, Taegu 702-701, Republic of KoreaDivision of General Education, Kwangwoon University, Seoul 139-701, Republic of KoreaWe derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x)∈ℚ[x]∣deg p(x)≤n} be the (n+1)-dimensional vector space over ℚ. Then we show that {H0(x),H1(x),…,Hn(x)} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications.http://dx.doi.org/10.1155/2012/974632 |
| spellingShingle | Dae San Kim Taekyun Kim Seog-Hoon Rim Sang Hun Lee Hermite Polynomials and their Applications Associated with Bernoulli and Euler Numbers Discrete Dynamics in Nature and Society |
| title | Hermite Polynomials and their Applications Associated with
Bernoulli and Euler Numbers |
| title_full | Hermite Polynomials and their Applications Associated with
Bernoulli and Euler Numbers |
| title_fullStr | Hermite Polynomials and their Applications Associated with
Bernoulli and Euler Numbers |
| title_full_unstemmed | Hermite Polynomials and their Applications Associated with
Bernoulli and Euler Numbers |
| title_short | Hermite Polynomials and their Applications Associated with
Bernoulli and Euler Numbers |
| title_sort | hermite polynomials and their applications associated with bernoulli and euler numbers |
| url | http://dx.doi.org/10.1155/2012/974632 |
| work_keys_str_mv | AT daesankim hermitepolynomialsandtheirapplicationsassociatedwithbernoulliandeulernumbers AT taekyunkim hermitepolynomialsandtheirapplicationsassociatedwithbernoulliandeulernumbers AT seoghoonrim hermitepolynomialsandtheirapplicationsassociatedwithbernoulliandeulernumbers AT sanghunlee hermitepolynomialsandtheirapplicationsassociatedwithbernoulliandeulernumbers |