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_…