Network


Latest external collaboration on country level. Dive into details by clicking on the dots.

Hotspot


Dive into the research topics where Shaun Cooper is active.

Publication


Featured researches published by Shaun Cooper.


International Journal of Number Theory | 2006

THE QUINTUPLE PRODUCT IDENTITY

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

Development of elliptic functions according to Ramanujan

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

Rational analogues of Ramanujan's series for 1/π

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

CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS

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

Sums of Five, Seven and Nine Squares

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

Relations between squares and triangles

Pierre Barrucand; Shaun Cooper; Michael D. Hirschhorn


Ramanujan Journal | 2000

Powers of Euler's Product and Related Identities

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

The Rogers-Ramanujan continued fraction and its level 13 analogue

Shaun Cooper; Dongxi Ye


Journal of Approximation Theory | 2002

The diagonalisation of the multivariate Bernstein operator

Shaun Cooper; Shayne Waldron

where


Bulletin of The Australian Mathematical Society | 2001

On some sum–to–product identities

Shaun Cooper; Michael D. Hirschhorn

Collaboration


Dive into the Shaun Cooper's collaboration.

Top Co-Authors

Avatar

Michael D. Hirschhorn

University of New South Wales

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Heng Huat Chan

National University of Singapore

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Pee Choon Toh

National University of Singapore

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Wen-Chin Liaw

National Chung Cheng University

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

B. Ramakrishnan

Harish-Chandra Research Institute

View shared research outputs
Top Co-Authors

Avatar

Sanoli Gun

Harish-Chandra Research Institute

View shared research outputs
Researchain Logo
Decentralizing Knowledge