A bound for certain bibasic sums and applications.
A combinatorial proof of a symmetric -Pfaff-Saalschütz identity.
A continued fraction expansion for a -tangent function: an elementary proof.
A continued fraction of order twelve
In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.
A de Casteljau algorithm for -Bernstein-Stancu polynomials.
A first order -difference system for the -type Jackson integral and its applications.
A note on an identity of Andrews.
A note on -partial difference equations and some applications to generating functions and -integrals
We study the condition on expanding an analytic several variables function in terms of products of the homogeneous generalized Al-Salam-Carlitz polynomials. As applications, we deduce bilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. We also gain multilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. Moreover, we obtain generalizations of Andrews-Askey integrals and Ramanujan -beta integrals. At last, we derive ...
A note on the multiple twisted Carlitz's type -Bernoulli polynomials.
A note on the -Genocchi numbers and polynomials.
A note on the Rogers-Fine identity.
A -congruence for a truncated series
Let denote the th cyclotomic polynomial in . Recently, Guo, Schlosser and Zudilin proved that for any integer with , where . In this note, we give a generalization of the above -congruence to the modulus case. Meanwhile, we give a corresponding -congruence modulo for . Our proof is based on the ‘creative microscoping’ method, recently developed by Guo and Zudilin, and a summation formula.
A sextuple product identity with applications.
A transformation formula for a special bilateral basic hypergeometric series.
Abel's method on Summation by Parets and Nonterminating q-Series Identities.
An inequality about and its applications.
An inequality about -Series.
An inequality and its -analogue.
An observation on the extension of Abel's lemma.
Approximate counting via Euler transform