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pro vyhledávání: '"Gong, Dianxuan"'
By means of the derivative operator and Chu-Vandermonde convolution, four families of summation formulas involving harmonic numbers with even or odd indexes are established.
Externí odkaz:
http://arxiv.org/abs/1806.09985
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 20 no. 2, Combinatorics (October 22, 2018) dmtcs:4476
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
Externí odkaz:
http://arxiv.org/abs/1804.11061
Autor:
Wei, Chuanan, Gong, Dianxuan
In 1981, Andrews gave a four-variable generalization of Ramanujan's ${_1\psi_1}$ summation formula. We establish a six-variable generalization of Andrews' identity according to the transformation formula for two ${_8\phi_7}$ series and Bailey's trans
Externí odkaz:
http://arxiv.org/abs/1301.4476
Autor:
Wei, Chuanan, Gong, Dianxuan
According to Abel's lemma and the method of linear combinations, we establish numerous contiguous relations of $_3\phi_2$-series, which can be regarded as q-analogues of the contiguous relations of $_3F_2$-series due to Krattenthaler and Rivoal [12]
Externí odkaz:
http://arxiv.org/abs/1209.2630
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
Externí odkaz:
http://arxiv.org/abs/1203.2863
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
Comment: This paper has been withdrawn by the author because that the main results of it are trivial
Comment: This paper has been withdrawn by the author because that the main results of it are trivial
Externí odkaz:
http://arxiv.org/abs/1203.2866
Autor:
Wei, Chuanan, Gong, Dianxuan
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 number identities including some known results.
Externí odkaz:
http://arxiv.org/abs/1203.2051
Autor:
Wei, Chuanan, Gong, Dianxuan
In terms of the hypergeometric method, we establish the extensions of two formulas for $1/\pi$ due to Ramanujan [27]. Further, other five summation formulas for $1/\pi$ with free parameters are also derived in the same way.
Externí odkaz:
http://arxiv.org/abs/1202.1029
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established.
Externí odkaz:
http://arxiv.org/abs/1201.0420
Autor:
Wei, Chuanan, Gong, Dianxuan
In this note, we show that Binomial theorem and Chu-Vandermonde convolution can both be verified by the finite difference method.
Externí odkaz:
http://arxiv.org/abs/1112.6221