New Harmonic Number Identities with Applications
نویسندگان
چکیده
We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums ∑n k=1 ∏r j=1Hk({1} ) when ∑r j=1 λj ≤ 5. We apply these identities to the study of two congruences modulo a power of a prime.
منابع مشابه
Riordan arrays and harmonic number identities
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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تاریخ انتشار 2010