On generalization of continued fraction of Gauss.
Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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On generalization of continued fraction of Gauss.
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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...