3 papers
math.CO2025
A Family of Congruences Modulo 7 for Partitions with Monochromatic Even Parts and Multi--Colored Odd Parts
Michael D. Hirschhorn, James A. Sellers
In recent work, Amdeberhan and Merca considered the integer partition function which counts the number of integer partitions of weight wherein even parts come in only on…
math.CA2016
A formula for the convergents of a continued fraction of Ramanujan
Gaurav Bhatnagar, Michael D. Hirschhorn
In Entry 16, Chapter 16 of his notebooks, Ramanujan himself gave a formula for the convergents of the famous Rogers-Ramanujan continued fraction. We provide a similar formula for t…
math.CA2012
A Refinement of Ramanujan's Factorial Approximation
Michael D. Hirschhorn, Mark B. Villarino
We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function