Hypergeometric series and harmonic number identities
نویسندگان
چکیده
منابع مشابه
87. Binomial Coefficient Identities and Hypergeometric Series
In recent months I have come across many instances in which someone has found what they believe is a new result, in which they evaluate in closed form a sum involving binomial coefficients or factorials. In each case they have managed to do that either by using the recent powerful method of Wilf and Zeilberger (the W–Z method) [6], or by comparing coefficients in some ad hoc algebraic identity....
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Let the numbers P (r, n, k) be defined by P (r, n, k) := Pr ( H n −H (1) k , · · · , H (r) n −H (r) k ) , where Pr(x1, · · · , xr) = (−1)Yr(−0!x1,−1!x2, · · · ,−(r− 1)!xr) and Yr are the exponential complete Bell polynomials. By observing that the numbers P (r, n, k) generate two Riordan arrays, we establish several general summation formulas, from which series of harmonic number identities are...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2005
ISSN: 0196-8858
DOI: 10.1016/j.aam.2004.05.003