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math.CA2022
Ramanujan's -continued fractions
Gaurav Bhatnagar
Ramanujan's -continued fractions are a central part of Ramanujan's development of basic hypergeometric series. They appear in Chapter 16 of Part III and Chapter 32 of Part V of…
math.CA2022
Telescoping continued fractions for the error term in Stirling's formula
Gaurav Bhatnagar, Krishnan Rajkumar
In this paper, we introduce telescoping continued fractions to find lower bounds for the error term in Stirling's approximation $\displaystyle n! = \sqrt{2π}n^{n+1/2}e^{-n}e^…