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math.CA2026
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_…
math.CA2023★ 1 cited
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…