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New definition of Bernoulli numbers
Author(s): 
Pages: 79-80
Year: Issue:  3
Journal: JOURNAL OF NANJING UNIVERSITY OF TECHNOLOGY(NATURAL SCIENCE EDITION)

Keyword:  幂级数等幂和递推公式:Bernoulli数;
Abstract: 无须利用幂级数而仅用定义或等幂和的一个递推公式直接给出Bernoulli数新的初等定义,其与经典的Bernoulli数相等,该定义的目的性明确且更加符合Jacobi.Bernoulli原来的想法,即证明了n-1∑k=0(nk)Bk=0,B0=1→←Sp(n-1)=1/p+1p∑k=0(p+1k)Bknp+1-k.
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