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**Date:** 2015
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1315924
**Description:** In celebration of both a special “big” π Day (3/14/15) and the 2015 centennial of the Mathematical Association of America, we review the illustrious history of the constant π in the pages of the Ameri... More
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**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.
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**Date:** 2014
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1303610
**Description:** The digits of π have intrigued both the public and research mathematicians from the beginning of time. This article briefly reviews the history of this venerable constant, and then describes some rece... More
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**Date:** 2012
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/939961
**Description:** We resolve and further study a sinc integral evaluation, first posed in this Monthly in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657]. After a short introduction ... More
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**Date:** 2010
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/933043
**Description:** It’s everywhere! It’s everywhere! … In this note we give elementary proofs of some of the striking asymptotic properties of the p-norm of the ubiquitous sinc function. Based on experimental evidence w... More
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**Date:** 2009
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940107
**Description:** We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases of a general approach to approximation. Herein we give ... More
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**Date:** 2008
**Resource Type:** journal article
**Identifier:** uon:5577
**Description:** The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the structure of the positive integers, such as: Every positive integer is the product of a unique finite... More
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**Creators:**
Borwein, Jonathan M.
**Date:** 2008
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940057
**Description:** In this article we explore a variety of pleasing connections between analysis, number theory, and operator theory, while revisiting a number of beautiful inequalities originating with Hilbert, Hardy a... More
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**Date:** 2008
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/940062
**Description:** We intend to show that a variety of trigonometric sums have unexpected closed forms by relating them to cognate integrals. We hope this offers a good advertisement for the possibilities of experimenta... More
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**Date:** 2006
**Keyword:** experimental mathematics | symbolic computation | numeric computation | mathematical discovery
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/928097
**Description:** This article presents and solves ten symbolic/numeric challenge problems, in the spirit of the recent SIAM hundred-digit, hundred-dollar challenge problems. Our goal in this article is to provide solu... More
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**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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**Date:** 1992
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1043650
**Description:** Five of the following twelve series approximations are exact. The remaining seven are not identities but are approximations that are correct to at least 30 digits. One in fact is correct to over 18,00... More
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**Date:** 1986
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.13/1043662
**Description:** In the course of a study of chemical lattice sums [1] the authors considered sums such as (1.1) ∑′ (- 1) ^{n+m+k} ( n^{2} + m^{2} + k^{2}) ^{-1/2}, the summatio... More
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