By Arnold Adelberg (auth.), Frederic T. Howard (eds.)

ISBN-10: 9048165458

ISBN-13: 9789048165452

This ebook includes 28 study articles from one of the forty nine papers and abstracts awarded on the 10th overseas convention on Fibonacci Numbers and Their purposes. those articles were chosen after a cautious assessment through professional referees, and so they variety over many parts of arithmetic. The Fibonacci numbers and recurrence family are their unifying bond. We be aware that the object "Fibonacci, Vern and Dan" , which follows the creation to this quantity, isn't a learn paper. it's a own memory by way of Marjorie Bicknell-Johnson, an established member of the Fibonacci organization. The editor believes it is going to be of curiosity to all readers. it's expected that this ebook, just like the 8 predecessors, may be important to investigate staff and scholars in any respect degrees who're attracted to the Fibonacci numbers and their functions. March sixteen, 2003 The Editor Fredric T. Howard arithmetic division Wake wooded area collage field 7388 Reynolda Station Winston-Salem, NC 27109 xxi THE ORGANIZING COMMITTEES neighborhood COMMITTEE overseas COMMITTEE Calvin lengthy, Chairman A. F. Horadam (Australia), Co-Chair Terry Crites A. N. Philippou (Cyprus), Co-Chair Steven Wilson A. Adelberg (U. S. A. ) C. Cooper (U. S. A. ) Jeff Rushal H. Harborth (Germany) Y. Horibe (Japan) M. Bicknell-Johnson (U. S. A. ) P. Kiss (Hungary) J. Lahr (Luxembourg) G. M. Phillips (Scotland) J. 'Thrner (New Zealand) xxiii xxiv record OF CONTRlBUTORS TO THE convention * ADELBERG, ARNOLD, "Universal Bernoulli Polynomials and p-adic Congruences. " *AGRATINI, OCTAVIAN, "A Generalization of Durrmeyer-Type Polynomials. " BENJAMIN, artwork, "Mathemagics.

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**Additional info for Applications of Fibonacci Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications**

**Sample text**

The aim of this Section is to point out the numerous possibilities regarding the structure of the function I{) when we choose the mentioned sequences. Firstly, we keep in mind the construction of I{) as a polynomial of degree less or equal to q(1{) E Pq ). We consider the sequences a and b such that beginning with the rank q they are definitively constant, which means an = a and bn = b for every n ~ q. After some manipulations, the relation (10) implies I{)(x) = a(1 - x)q + bx q + x(1 - q-l x) L (a m (1- x)m-l + bm x m - 1 ), m=l The relations (13) and (14) will have a new look, that is /len) = /l(q) and v(n) = and consequently, for every a, n = q,q+ l,q+ 2, ...

0 Remark: From (7) we deduce (Mneo)(O) = an and (Mneo)(l) = bn . This means that the convergence of (Mn)n~1 implies the convergence of the sequences a and b. In what follows we assume that these sequences converge and set lim bn = h. lim an = la, n-+oo (9) n-+oo Because of the above assumption we can define the functions follows x =0, T(X) = { O

3 (2000): pp. 282-288. T. A. " Applications of Fibonacci Numbers. Volume 10. Edited by Fredric T. Howard. Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003: pp. 25-28. [5] Carlitz, L. " The Fibonacci Quarterly, Vol. 2 (1965): pp. 81-89. F. L. C. " American Mathematical Monthly, Vol. 8 (1991): pp. 719-727. [7] Larson, L. " Mathematics Magazine, Vol. 2 (1991): pp. 141-144. N. " The Fibonacci Quarterly, Vol. 2 (1983): pp. 82-86. A. " The Fibonacci Quarterly, Vol. 1 (1982): pp. 28-32. P.