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Dianxuan Gong

Publications and source records attributed to Dianxuan Gong.

13 recordsLinked to original sources
arXiv2020

Several transformation formulas for basic hypergeometric series

In 1981, Andrews gave a four-variable generalization of Ramanujan's ${_1ψ_1}$ summation formula. We establish a six-variable generalization of Andrews' identity according to the transformation formula for two ${_8ϕ_7}$ series and Bailey's transformation formula for three ${_8ϕ_7}$ series. Then it is used to find a six-variable generalization of Ramanujan's reciprocity theorem, which is different from Liu's formula. We derive the generalizations of Bailey's two $_3ψ_3$ summation formulas in terms of two limiting relations and Bailey's another transformation formula for three $_8ϕ_7$ series. Based on the two limiting relations, some different results involving bilateral basic hypergeometric series are also deduced from the Guo--Schlosser transformation formula and other two transformation formulas.

math.CA↗
arXiv2018

Summation formulas for Fox-Wright function

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.

math.CO↗
arXiv2012

Contiguous relations of $_3ϕ_2$-series

According to Abel's lemma and the method of linear combinations, we establish numerous contiguous relations of $_3ϕ_2$-series, which can be regarded as q-analogues of the contiguous relations of $_3F_2$-series due to Krattenthaler and Rivoal [12] or Chu and Wang [4].

math.CA↗
arXiv2012

$π$-formulas with free parameters

In terms of the hypergeometric method, we give the extensions of two known series for $π$. Further, other twenty-nine summation formulas for $π$, $π^2$ and $1/π$ with free parameters are also derived in the same way.

math.CO↗
arXiv2012

Extensions of Ramanujan's two formulas for $1/π$

In terms of the hypergeometric method, we establish the extensions of two formulas for $1/π$ due to Ramanujan [27]. Further, other five summation formulas for $1/π$ with free parameters are also derived in the same way.

math.CO↗
arXiv2011

Derivative operator and harmonic number identities

By applying the derivative operator to the corresponding hypergeometric form of a $q$-series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number identity. As the special cases of it, several interesting Chu-Donno type identities and Paule-Schneider type identities are displayed.

math.CO↗