Roy received a BS degree from the Indian Institute of Technology Kharagpur, an MS in mathematics from the Indian Institute of Technology Kanpur, and a PhD at Stony Brook University.
After receiving his PhD, Roy taught at the University of Kentucky for a short time, then returned to India where he took posts at the Indian Institute of Technology Delhi and Himachal Pradesh University, and received a fellowship at the Indian Institute of Advanced Study.
In 1982, Roy joined Beloit College, spending the rest of his career there.
[2] Roy published many papers on differential equations, fluid mechanics, special functions, Fuchsian groups, and the history of mathematics.
He is a coauthor of the book Special Functions (with G. E. Andrews and R. Askey), published by Cambridge University Press in 1999.