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Contiguous relations of -series
Chuanan Wei, Dianxuan Gong
According to Abel's lemma and the method of linear combinations, we establish numerous contiguous relations of -series, which can be regarded as q-analogues of the contiguou…
A family of summation formulas involving generalized harmonic numbers
Chuanan Wei, Qinglun Yan, Dianxuan Gong
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
Telescoping method, derivative operators and harmonic number identities
Chuanan Wei, Dianxuan Gong
In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several general harmonic numbe…
A class of summation formulas on generalized harmonic numbers
Chuanan Wei, Dianxuan Gong, Qinglun Yan
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
Extensions of Ramanujan's two formulas for
Chuanan Wei, Dianxuan Gong
In terms of the hypergeometric method, we establish the extensions of two formulas for due to Ramanujan [27]. Further, other five summation formulas for with free param…
Chu-Vandermonde convolution and harmonic number identities
Chuanan Wei, Dianxuan Gong, Qin Wang
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established.