13 citations · 39 across the 19 of their papers we have counts for
21 papers
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…
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^…
Expansion formulas for multiple basic hypergeometric series over root systems
Gaurav Bhatnagar, Surbhi Rai
We extend expansion formulas of Liu given in 2013 to the context of multiple series over root systems. Liu and others have shown the usefulness of these formulas in Special Functio…
Stanley--Elder--Fine theorems for colored partitions
Hartosh Singh Bal, Gaurav Bhatnagar
We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored parti…
Glaisher's divisors and infinite products
Hartosh Singh Bal, Gaurav Bhatnagar
Ramanujan gave a recurrence relation for the partition function in terms of the sum of the divisor function . In 1885, J.W. Glaisher considered seven divisor sums closely rel…
The Partition-Frequency Enumeration Matrix
Hartosh Singh Bal, Gaurav Bhatnagar
We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the Part…