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Some identities for generalized harmonic numbers

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Koparal, Sibel
Ömür, N.
Sudemen, K. N.

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Math Soc Serbia-drustvo Matematicara Srbije

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In this paper, we derive some nonlinear differential equations from generating function of generalized harmonic numbers and give some identities involving generalized harmonic numbers and special numbers by using these differential equations. For example, for any positive integers N, n, r, alpha and any integer m >= 2, S1(n + N, r + 1) n ! n X = j=0 n X i=0 i X l=0 l X z=0 r X k=0 ! ! N j alpha i (1)l-z-i m i l + m 2 l z i l j! ( n i)! x S1(N, r k + 1) S 1 ( n i, k) H(z, j 1 , alpha) where S 1 ( n, k ) is Stirling number of the first kind.

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Sums, Generalized hyperharmonic numbers of order r, Daehee numbers, Stirling numbers of the first kind and the second kind, Generating function, Science & technology, Physical sciences, Mathematics

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