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Exploration of Fibonacci Function

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Abstract:

In this paper, I define Fibonacci function (probably unknown) on Real number field, for all x∈R, F:R → R,э F (x+n) = nF(x+1)+n-1F(x). Also, I defined the limit value of Fibonacci function, which is closed to 1.618… where x tends to infinity. Including, Fibonacci sum as well.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 1)
Pages:
57-62
DOI:
10.18052/www.scipress.com/BMSA.1.57
Citation:
K. R. R. Gandhi "Exploration of Fibonacci Function", Bulletin of Mathematical Sciences and Applications, Vol. 1, pp. 57-62, 2012
Online since:
Aug 2012
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References:

http: /www. mathsisfun. com/numbers/golden-ratio. html.

http: /en. wikipedia. org/wiki/Fibonacci_number.

http: /mathworld. wolfram. com/FibonacciNumber. html.

http: /sajm. com. nu/sajm2011_1_3_8gandhi. pdf.

http: /ulcar. uml. edu/~iag/CS/Fibonacci. html.

http: /www. artofproblemsolving. com/Forum/viewtopic. php?f=36&p=2084357#p.2084357.

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