  
  
Stat 
Members: 2708 Articles: 1'972'659 Articles rated: 2572
16 July 2020 

   

Article overview
 

Identities concerning Bernoulli and Euler polynomials  ZhiWei Sun
; Hao Pan
;  Date: 
2 Sep 2004  Subject:  Number Theory; Combinatorics MSCclass: 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 $$F(s,t;x,y):=sum_{k=0}^n(1)^kinom{s}{k}inom{t}{nk}B_{nk}(x)B_k(y).$$ This symmetric relation implies the curious identities of Miki and Matiyasevich as well as some new identities for Bernoulli polynomials such as $$sum_{k=0}^ninom{n}{k}^2B_k(x)B_{nk}(x)=2sum^nSb k=0 k
ot=n1endSbinom{n}{k}inom{n+k1}{k}B_k(x)B_{nk}.$$  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 CCBot/2.0 (https://commoncrawl.org/faq/)

 



 News, job offers and information for researchers and scientists:
 