1 citations · 1 across the 5 of their papers we have counts for
5 papers
Notices on a new functional identity and allied series transformations
Jianan Xu, Qi Chen
In this paper, we establish an elementary functional identity \begin{align*}\sum_{k=1}^{n}\bigg(\frac{f(a,d_k)}{f(a,x)}\bigg)^{n-1}\prod_{i=1,i \neq k}^{n} \frac{g(x,d_i)}{g(d_k,d_…
Two new Bailey pairs and their -identities of Rogers-Ramanujan type modulo 15, 24, and 30
Jianan Xu, Xinrong Ma
In this paper, we first establish two new Bailey pairs via finding two generalizations of Euler's pentagonal number theorem. Next, we specificize the Bailey lemmas with these two B…
A general -series transformation and its applications to multi-sum Rogers-Ramanujan-Slater identities
Jianan Xu, Xinrong Ma
In the present paper, we establish a general transformation for -series which contains L. Wang et al's transformation involved in Nahm series. As direct applications, some concr…
Three new -Abel transformations and their applications
Jianan Xu, Xinrong Ma
In the present paper, we establish three special -Abel transformation formulae of -series via the use of Abel's lemma on summation by parts. As direct applications, we set up…
General -series transformations based on Abel's lemma on summation by parts and their applications
Jianan Xu, Xinrong Ma
In this paper, we establish three new and general transformations with sixteen parameters and bases via Abel's lemma on summation by parts. As applications, we set up a lot of new…