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Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1174269
Description: In the current work ultraviolet spectrophotometric titrations at different S₍ᵢᵥ₎ concentrations have been globally analysed using the entire spectral dataset to determine the complete speciation of S₍... More
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Date: 1993
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940950
Description: We show that L1(µ) has a weak Hadamard differentiable renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if µ is sigma finite. As a consequen... More
Reviewed: Reviewed
Creators: Borwein, Jon
Date: 1985
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940539
Description: We show how various modular identities due to Ramanujan may be used to produce simple high order approximations to π. Various specializations are considered and the Gaussian arithmetic geometric mean ... More
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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: Reviewed
Creators: Zudilin, W.
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/934854
Description: Some of the most spectacular achievements in the history of the number π are the representations of 1/π by rapidly converging series discovered by Ramanujan in 1914. Although Ramanujan himself did not... More
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Date: 1993
Keyword: Ramanujan | series | pi | class number
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940980
Description: There is a class of remarkable series for 1/π of the form [formula could not be replicated] where A, B, C are certain algebraic numbers. These were first examined by Ramanujan. These examples arise by... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1039906
Description: We recently concluded a very large mathematical calculation, uncovering objects that until recently were widely considered to be forever inaccessible to computation. Our computations stem from the “BB... More
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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: Reviewed
Creators: Zudilin, W.
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/934847
Description: We prove two new series of Ramanujan type for 1/π².
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Date: 1986
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1043612
Description: We present a quadratically converging algorithm for π based on a formula of Legendre's for complete elliptic integrals of modulus sin(π/12) and the arithmetic-geometric mean iteration of Gauss and Leg... More
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Date: 2012
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/940028
Description: Using the results of several extremely large recent computations [Yee and Kondo 11], we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of π. This result was us... More
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Creators: Chan, HH | Wan, G | Zudilin, V
Date: 2012
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/936507
Description: Many series for 1/π were discovered since the appearance of S. Ramanujan's famous paper "Modular equations and approximation to π" published in 1914. Almost all these series involve only real numbers.... More
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Creators: Borwein, JM | Borwein, PB
Date: 1983
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1042404
Description: There has recently been considerable interest in an essentially quadratic method for computing π. The algorithm, first suggested by Salamin, is based upon an identity known to Gauss. This iteration ha... More
Creators: Bundschuh, P | Zudilin, W
Date: 2008
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.13/1054222
Reviewed: Reviewed
Creators: Chan, HH | Wan, J | Zudilin, W
Date: 2013
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/1039866
Description: We resolve a family of recently observed identities involving 1/π using the theory of modular forms and hypergeometric series. In particular, we resort to a formula of Brafman which relates a generati... More
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