Yazar "Stakhov, Alexey" seçeneğine göre listele

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    Bivariate fibonacci like p-polynomials
    (ELSEVIER SCIENCE INC, 2011) Tuglu, Naim; Kocer, E. Gokcen; Stakhov, Alexey
    In this article, we study the bivariate Fibonacci and Lucas p-polynomials (p >= 0 is integer) from which, specifying x, y and p, bivariate Fibonacci and Lucas polynomials, bivariate Pell and Pell-Lucas polynomials, Jacobsthal and Jacobsthal-Lucas polynomials, Fibonacci and Lucas p-polynomials, Fibonacci and Lucas p-numbers, Pell and Pell-Lucas p-numbers and Chebyshev polynomials of the first and second kind, are obtained. Afterwards, we obtain some properties of the bivariate Fibonacci and Lucas p-polynomials. (C) 2011 Elsevier Inc. All rights reserved.
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    Hyperbolic functions with second order recurrence sequences
    (CHARLES BABBAGE RES CTR, 2008) Kocer, E. Gokcen; Tuglu, Naim; Stakhov, Alexey
    In this paper, we introduce an extension of the hyperbolic Fibonacci and Lucas functions which were studied by Stakhov and Rozin. Namely, we define hyperbolic functions by second order recurrence sequences and study their hyperbolic and recurrence properties. We give the corollaries for Fibonacci, Lucas, Pell and Pell-Lucas numbers. We finalize with the introduction some surfaces (the Metallic Shofars) that relate to the hyperbolic functions with the second order recurrence sequences.
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    On the m-extension of the Fibonacci and Lucas p-numbers
    (PERGAMON-ELSEVIER SCIENCE LTD, 2009) Kocer, E. Gokcen; Tuglu, Naim; Stakhov, Alexey
    In this article, we define the m-extension of the Fibonacci and Lucas p-numbers (p >= 0 is integer and m >= 0 is real number) from which, specifying p and in, classic Fibonacci and Lucas numbers (p = 1, m = 1), Pell and Pell-Lucas numbers (p = 1, m = 2), Fibonacci and Lucas p-numbers (m = 1), Fibonacci in-numbers (p = 1), Pell and Pell-Lucas p-numbers (m = 2) are obtained. Afterwards, we obtain the continuous functions for the m-extension of the Fibonacci and Lucas p-numbers using the generalized Binet formulas. Also we introduce in the article a new class of mathematical constants - the Golden (p,m)-Proportions, which are a wide generalization of the classical golden mean, the golden p-proportions and the golden m-proportions. The article is of fundamental interest for theoretical physics where Fibonacci numbers and the golden mean are used widely. (c) 2007 Elsevier Ltd. All rights reserved.