| | |
| | |
Stat |
Members: 3645 Articles: 2'504'585 Articles rated: 2609
24 April 2024 |
|
| | | |
|
Article overview
| |
|
Identities concerning Bernoulli and Euler polynomials | Zhi-Wei Sun
; Hao Pan
; | Date: |
2 Sep 2004 | Subject: | Number Theory; Combinatorics MSC-class: 11B68; 05A19 | math.NT math.CO | Abstract: | We establish two general identities for Bernoulli and Euler polynomials, these identities of a new type have many consequences. The most striking result in this paper is as follows: If $n$ is a positive integer, $r+s+t=n$ and $x+y+z=1$, then we have $$rF(s,t;x,y)+sF(t,r;y,z)+tF(r,s;z,x)=0$$ where $$F(s,t;x,y):=sum_{k=0}^n(-1)^kinom{s}{k}inom{t}{n-k}B_{n-k}(x)B_k(y).$$ This symmetric relation implies the curious identities of Miki and Matiyasevich as well as some new identities for Bernoulli polynomials such as $$sum_{k=0}^ninom{n}{k}^2B_k(x)B_{n-k}(x)=2sum^nSb k=0 k
ot=n-1endSbinom{n}{k}inom{n+k-1}{k}B_k(x)B_{n-k}.$$ | Source: | arXiv, math.NT/0409035 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |