arXiv subjects
Publications and source records attributed to Chuanan Wei.
Solutions of Pell's equation and hypergeometric series identities are used to study series expansions for $\sqrt{p}$ where $p$ are arbitrary prime numbers. Numerous fast convergent series expansions for this family of irrational numbers are established.
According to the method of series rearrangement, we establish the extensions of two $q$-Gosper identities with an extra integer parameter. The limiting cases of them produce the generalizations of Gosper's two $_3F_2(\frac{3}{4})$-series identities with an additional integer parameter. Meanwhile, several related results are also given.
According to the method of series rearrangement, we establish two generalizations of Andrews' curious $q$-series identity with an extra integer parameter. The limiting cases of them produce two extensions of Andrews' curious $_3F_2(\frac{3}{4})$-series identity with an additional integer parameter. Meanwhile, several related results are also given.
By means of the telescoping method, we establish two sum- mation formulas on sine function. As the special cases of them, several interesting series expansions for $1/π^m$ and $π^m$.
In terms of Sear's transformation formula for $_4ϕ_3$-series, we give new proofs of a summation formula for ${_4ϕ_3}$-series due to Andrews [2] and another summation formula for${_4ϕ_3}$-series conjectured in the same paper. Meanwhile, other several related results are also derived.
By using two known transformation formulas for basic hypergeometric series, we establish a direct extension of Bailey's $_6ψ_6$-series identity. Subsequently, it and Milne's identity are employed to drive multi-variable generalizations of Ramanujan's reciprocity formula. Then we utilize also Milne's identity to deduce a multi-variable generalization of the Askey-Wilson integral.
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
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].
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
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.
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.
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established.
In this note, we show that Binomial theorem and Chu-Vandermonde convolution can both be verified by the finite difference method.
According to the method of series rearrangement, we establish two families of summation formulae for $q$-Watson type $_4ϕ_3$-series.
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.
According to Chen and Fu's method, we offer a short proof for Dougall's $_2H_2$-series identity.