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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1329529
Description: This paper extends tools developed to study character polylogarithms. These objects are used to compute Mordell–Tornheim–Witten character sums and to explore their connections with multiple-zeta value... More
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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1338273
Description: In this paper, we study maximal monotone inclusions from the perspective of gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion and will demonstrat... More
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Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1339388
Description: In Bailey etal. [8] the current authors, along with the late and much-missed Richard Crandall (1947-2012), considered generalized Mordell-Tornheim-Witten (MTW) zeta-function values along with their de... More
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Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1329486
Description: This paper extends tools developed by Crandall (2012) [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to... More
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Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940012
Description: In recent times, attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical). Herein we ... More
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Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/939951
Description: At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications... More
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Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1038229
Description: One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Gedde... More
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Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1038088
Description: We undertake a thorough investigation of the moments of Ramanujanʼs alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed for... More
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Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/932067
Description: Box integrals - expectations 〈|r→|s or 〈|r→ - q→|s〉 over the unit n-cube - have over three decades been occasionally given closed forms for isolated n, s. By employing experimental mathematics togethe... More
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Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/807948
Description: Herein we develop connections between zeta functions and some recent "mysterious" constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz [Qu... More
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Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940063
Description: It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represe... More
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Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/928076
Description: Euler considered sums of the form [formula unable to be reproduced here]. Here natural generalizations of these sums namely [formula unable to be reproduced here], are investigated, where χ p and χ q ... More
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Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940735
Description: By a “box integral” we mean here an expectation <|→/r − →/q|s> where →/r runs over the unit n-cube, with →/q and s fixed, explicitly: ∫₀¹...∫₀¹((r₁-q₁)²+...+(rn-qn)²)s/2... More
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Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/926999
Description: We apply experimental-mathematical principles to analyze the integrals [[unable to reproduce here]]. These are generalizations of a previous integral Cn := Cn,1 relevant to the Ising theory of solid-s... More
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Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/803609
Description: From an experimental-mathematical perspective we analyse 'Ising-class' integrals. These are structurally related n-dimensional integrals we call Cn, Dn, En, where Dn is a magnetic susceptibility integ... More
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