The method of telescoping continued fractions

Gaurav Bhatnagar, Krishnan Rajkumar

We give an approach to discover continued fractions for series of the form $$\sum _{k=0}^{\infty }\frac{{\epsilon }^k}{(x+k{)}^s},$$ where $\epsilon =\pm 1$. We find a continued fraction of the form \be…