Elementary proof of Yu. V. Nesterenko expansion of the number zeta(3) in continued fraction.
Gutnik, Leonid (2010)
Advances in Difference Equations [electronic only]
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Displaying similar documents to “An Apéry-like difference equation for Catalan's constant.”
Elementary proof of Yu. V. Nesterenko expansion of the number zeta(3) in continued fraction.
Computation of -partial fractions.
Munagi, Augustine O. (2007)
Integers
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On the Ramanujan AGM fraction. II: The complex-parameter case.
Borwein, J., Crandall, R. (2004)
Experimental Mathematics
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Hurwitz continued fractions with confluent hypergeometric functions
Takao Komatsu (2007)
Czechoslovak Mathematical Journal
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Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.
On a combinatorial problem of Asmus Schmidt.
Zudilin, W. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Evaluation of the Fermi-Dirac integral of half-integer order
S. Paszkowski (1991)
Applicationes Mathematicae
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On a theorem of Legendre in the theory of continued fractions
Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Searching for strange hypergeometric identities by sheer brute force.
Apagodu, Moa, Zeilberger, Doron (2008)
Integers
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On the length of the continued fraction for values of quotients of power sums
Pietro Corvaja, Umberto Zannier (2005)
Journal de Théorie des Nombres de Bordeaux
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Generalizing a result of Pourchet, we show that, if are power sums over satisfying suitable necessary assumptions, the length of the continued fraction for tends to infinity as . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers , .
Beukers' integrals and Apéry's recurrences.
Jain, Lalit, Tzermias, Pavlos (2005)
Journal of Integer Sequences [electronic only]
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An objective and practical method for describing and understanding ratios
D. H. Fowler (1993)
Mathématiques et Sciences Humaines
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This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.