Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 2896
Articles: 1'996'896
Articles rated: 2574

22 September 2020
 
  » » arxiv » 244469

 Article forum


On sums of binomial coefficients and their applications
Zhi-Wei Sun ;
Date 21 Apr 2004
Subject Number Theory; Combinatorics MSC-class: 11B65; 05A19; 11B37; 11B68 | math.NT math.CO
AbstractIn this paper we study recurrences concerning the combinatorial sum $S(n,r)=sum_{kequiv r (mod m)}inom {n}{k}$ and the alternate sum $sum_{kequiv r (mod m)}(-1)^{(k-r)/m}inom{n}{k}$, where $m>0$, $nge 0$ and $r$ are integers. For example, we show that if $nge m-1$ then $$sum_{i=0}^{lfloor(m-1)/2 floor}(-1)^iinom{m-1-i}i S(n-2i,r-i)=2^{n-m+1}.$$ We also apply such results to investigate Bernoulli and Euler polynomials. Our approach depends heavily on an identity given by the author [Integers 2(2002)].
Source arXiv, math.NT/0404385
Services Forum | Review | PDF | Favorites   
 

No message found in this article forum.  You have a question or message about this article? Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..

Subject of your forum message:
Write your forum message below (min 50, max 2000 characters)

2000 characters left.
Please, read carefully your message since you cannot modify it after submitting.

  To add a message in the forum, you need to login or register first. (free): registration page






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2020 - Scimetrica