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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
Reviewed: 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: Reviewed
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
Reviewed: Reviewed
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a sinc integral evaluation, first posed in this Monthly in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657].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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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
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 ( n2 + m2 + k2) -1/2, the summatio... More
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