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**Creators:**
Aragón Artacho, Francisco J.
**Date:** 2007
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/933719
**Description:** Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended ve... More
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**Reviewed:**
**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1295837
**Description:** Motivated by questions of algorithm analysis, we provide several distinct approaches to determining convergence and limit values for a class of linear iterations.
**Reviewed:**
**Date:** 2007
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940746
**Description:** We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.
**Reviewed:**
**Date:** 1988
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/941074
**Description:** This contribution highlights the progress made regarding Ramanujan's work on Pi since the centennial of his birth in 1987.
**Date:** 1986
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/941059
**Description:** Using the theory of the cubic modular equation we have discovered a remarkably simple class of cubically convergent algebraic iterations for π.
**Reviewed:**
**Date:** 1984
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940986
**Description:** We show that the theory of elliptic integral transformations may be employed to construct iterative approximations for π of order p (p any prime). Details are provided for two, three and seven. The cu... More
**Reviewed:**
**Date:** 1998
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1037938
**Description:** Borwein and Wang show that the converse of the classical mean value theorem may fail generically.
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**Reviewed:**
**Date:** 2008
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940072
**Description:** We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the conti... More
**Reviewed:**
**Creators:**
Borwein, J. M.
**Date:** 1983
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1042399
**Description:** We present a development of the Farkas lemma which is particularly suited for presentation in the classroom
**Reviewed:**
**Date:** 2013
**Keyword:** gamma function | log-gamma function | Riemann zeta function | Tornheim–Weitten zeta function | integration
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940016
**Description:** Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., 139(2):535-545, 2010), we evaluate various basic log Gamma integrals in terms of partial derivatives of T... More
**Reviewed:**
**Date:** 2009
**Language:** eng
**Resource Type:** book
**Identifier:** http://hdl.handle.net/1959.13/917802
**Description:** Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces t... More
**Date:** 2006
**Keyword:** Riemann zeta function | central binomial coefficients | series acceleration | hypergeometric series
**Resource Type:** journal article
**Identifier:** uon:6476
**Description:** We document the discovery of two generating functions for ζ(2n+2), analogous to earlier work for ζ(2n+1) and ζ(4n+3), initiated by Koecher and pursued further by Borwein, Bradley, and others.
**Reviewed:**
**Date:** 2006
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/926998
**Description:** We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these ... More
**Reviewed:**
**Date:** 2002
**Keyword:** multi-variable sinc integrals | Fourier transforms | convolution | Parseval's theorem | volumes of polyhedra
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940675
**Description:** We investigate multi-variable integrals of products of sinc functions and show how they may be interpreted as volumes of symmetric convex polyhedra. We then derive an explicit formula for computing su... More
**Reviewed:**
**Date:** 2001
**Keyword:** psi function | gamma function | modified convexity | volume of p balls | substitution norm | Blaschke Santalo inequality
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940694
**Description:** We derive the l_{p} version of the classical Blaschke-Santalo inequality for polar volumes as a consequence of more subtle convexity estimates for the volume of the p -ball in Euclidean space.... More
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