Shaun Cooper
Massey University
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Publication
Featured researches published by Shaun Cooper.
International Journal of Number Theory | 2006
Shaun Cooper
The quintuple product identity was first discovered about 90 years ago. It has been published in many different forms, and at least 29 proofs have been given. We shall give a comprehensive survey of the work on the quintuple product identity, and a detailed analysis of the many proofs.
Archive | 2011
K Venkatachaliengar; Shaun Cooper
Generalized Ramanujan Identity Weierstrass Elliptic Function Ramanujans Differential Equations, Ramanujans 1-Psi-1 Summation Formula Jacobi Triple Product Identity Jordan - Kronecker Function Fundamental Multiplicative Identity Hypergeometric Functions Halphens Differential Equations Sums of Two and Four Squares Ramanujans Theories of Elliptic Functions to Alternative Bases Jacobian Elliptic Functions Modular Equations Addition Theorem for Elliptic Integrals Quintuple Product Identity.
Mathematical Proceedings of the Cambridge Philosophical Society | 2012
Heng Huat Chan; Shaun Cooper
A general theorem is stated that unifies 93 rational Ramanujan-type series for 1/π, 40 of which are believed to be new. Moreover, each series is shown to have a companion identity, thereby giving another 93 series, the majority of which are new.
International Journal of Number Theory | 2010
Heng Huat Chan; Shaun Cooper; Francesco Sica
HENG HUAT CHAN∗, SHAUN COOPER† and FRANCESCO SICA‡ ∗Department of Mathematics, National University of Singapore Block S17, 10, Lower Kent Ridge Road, 119076 Singapore [email protected] †Institute of Information and Mathematical Sciences Massey University, Private Bag 102904 North Shore Mail Centre, Auckland, New Zealand [email protected] ‡Mathematics and Computer Science, Mount Allison University 67 York Street, Sackville, NB, E4L 1E6, Canada [email protected]
Ramanujan Journal | 2002
Shaun Cooper
AbstractLet rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that
Discrete Mathematics | 2002
Pierre Barrucand; Shaun Cooper; Michael D. Hirschhorn
Ramanujan Journal | 2000
Shaun Cooper; Michael D. Hirschhorn; Richard Lewis
\begin{gathered} r_5 \left( n \right) = r_5 \left( {n\prime } \right)\left[ {\frac{{2^{3\left\lfloor {\lambda /2} \right\rfloor + 3} - 1}}{{2^3 - 1}} - \varepsilon _5 \left( {n\prime } \right)\frac{{2^{3\left\lfloor {\lambda /2} \right\rfloor } - 1}}{{2^3 - 1}}} \right] \hfill \\ {\text{ }} \times \mathop \prod \limits_p \left[ {\frac{{p^{3\left\lfloor {\lambda p/2} \right\rfloor + 3} - 1}}{{p^3 - 1}} - p\left( {\frac{{n\prime }}{p}} \right)\frac{{p^{3\left\lfloor {\lambda p/2} \right\rfloor } - 1}}{{p^3 - 1}}} \right], \hfill \\ \end{gathered}
Journal of Approximation Theory | 2015
Shaun Cooper; Dongxi Ye
Journal of Approximation Theory | 2002
Shaun Cooper; Shayne Waldron
where
Bulletin of The Australian Mathematical Society | 2001
Shaun Cooper; Michael D. Hirschhorn