Shaun Cooper

collaborators

2 papers

math.NT2026

Quadratic irrational analogues of Ramanujan's series for $1/ I ¨ $

John M. Campbell, Shaun Cooper, Dongxi Ye

About 40 years ago Jonathan and Peter Borwein discovered the series identity $n = 0 \sum \infty \frac{( - 1 ) ^{n} ( 6 n )!}{( 3 n )! ( n ! ) ^{3}} \frac{( A + n B )}{C ^{n + 1/2}} = \frac{1}{12 I ¨ }$ where…

math.NT2025

Ramanujan--Fine integrals for level 10

Shaun Cooper, Timothy Huber, Jeffery Opoku

We investigate the question of when an eta quotient is a derivative of a formal power series with integer coefficients and present an analysis in the case of level 10. As a consequ…

Quadratic irrational analogues of Ramanujan's series for 1/I¨

Ramanujan--Fine integrals for level 10

Quadratic irrational analogues of Ramanujan's series for $1/ I ¨ $