Volume 5, Issue 7 (July 2018), Pages: 58-63

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 Original Research Paper

 Title: On the extension of generalized Fibonacci function

 Author(s): Krishna Kumar Sharma *

 Affiliation(s):

 School of Vocational Studies and Applied Sciences, Gautam Buddha University, Greater Noida (U.P.), India

 https://doi.org/10.21833/ijaas.2018.07.008

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 Abstract:

The Fibonacci sequence is well known for having many hidden patterns within it. The famous mathematical sequence 1,1,2,3,5,8,13,21,34,55,89,. . m, n, m +n . . . known as the Fibonacci sequence F_n+1=F_n+F_n-1  ,n≥1,F₁=F₂=1,  It has been discovered in many places such as nature, art and even in music. It has an incredible relationship with the golden ratio. In this paper, we define Fibonacci function on real number field for all real x,f: R→R, there exist f(x+n)=a f(x+n-1)+b f(x+n-2) . We developed the notion of generalized Fibonacci function using the concept of Binet's formula and induction technique and construct the relation between generalized Fibonacci function and generalized Fibonacci numbers. We also develop the notion of generalized Fibonacci functions with period s using the concept of f -even and f -odd functions. 

 © 2018 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Fibonacci numbers, Generalized Fibonacci numbers, Generalized Fibonacci function

 Article History: Received 12 December 2017, Received in revised form 23 April 2018, Accepted 28 April 2018

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2018.07.008

 Citation:

 Sharma KK (2018). On the extension of generalized Fibonacci function. International Journal of Advanced and Applied Sciences, 5(7): 58-63

 Permanent Link:

 http://www.science-gate.com/IJAAS/2018/V5I7/Sharma.html

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