Some more long continued fractions, I
James Mc Laughlin, Peter Zimmer (2007)
Acta Arithmetica
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James Mc Laughlin, Peter Zimmer (2007)
Acta Arithmetica
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Jacobson, Michael J.jun., Williams, Hugh C. (2000)
Experimental Mathematics
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Kell Cheng, Hugh Williams (2005)
Acta Arithmetica
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A. Schinzel (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is proved that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence Bₙ(1). As an application, the degree of Bₙ(t) is expressed in terms of the binary expansion of n.
Stein, Andreas, Williams, Hugh C. (1999)
Experimental Mathematics
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D. Bowman, J. Mc Laughlin (2002)
Acta Arithmetica
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Toufik Mansour (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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We present a q-analogue for the fact that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. Moreover, we give a combinatorial interpretation for our q-analogue.
Edward B. Burger, David C. Clyde, Cory H. Colbert, Gea Hyun Shin, Zhaoning Wang (2012)
Acta Arithmetica
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Mollin, Richard A. (1990)
International Journal of Mathematics and Mathematical Sciences
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E. FRANK (1969)
Mathematische Annalen
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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...
E. FRANK (1962/63)
Numerische Mathematik
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E. FRANK (1962/63)
Numerische Mathematik
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E. FRANK (1963)
Numerische Mathematik
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