On generalization of continued fraction of Gauss.
Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Heng Huat Chan, Kok Ping Loo (2007)
Acta Arithmetica
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Sebe, Gabriela Ileana (2005)
International Journal of Mathematics and Mathematical Sciences
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Boonrod Yuttanan (2012)
Acta Arithmetica
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Takao Komatsu (2003)
Acta Arithmetica
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Shaun Cooper (2010)
Acta Arithmetica
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Komatsu, Takao (2004)
Mathematica Pannonica
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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.
James Mc Laughlin (2008)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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J. Mc Laughlin, Nancy J. Wyshinski (2005)
Acta Arithmetica
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Anton Lukyanenko, Joseph Vandehey (2015)
Acta Arithmetica
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We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
S. G. Dani (2015)
Acta Arithmetica
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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...