International journal of


EISSN: 2313-3724, Print ISSN:2313-626X

Frequency: 12

line decor
line decor

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


 Original Research Paper

 Title: On the extension of generalized Fibonacci function

 Author(s): Krishna Kumar Sharma *


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

 Full Text - PDF          XML


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 Fn+1=Fn+Fn-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 (

 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:


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

 Permanent Link:


 References (6) 

  1. Elmore M (1967). Fibonacci functions. Fibonacci Quarterly, 5(4): 371-382.   [Google Scholar]  
  2. Gandhi KRR (2012). Exploration of fibonacci function. Bulletin of Mathematical Sciences and Applications, 1(1): 77-84.   [Google Scholar] 
  3. Han JS, Kim HS, and Neggers J (2012). On Fibonacci functions with Fibonacci numbers. Advances in Difference Equations, 2012: 126.   [Google Scholar] 
  4. Parker FD (1968). A fibonacci function. The Fibonacci Quarterly, 6(1): 1-2.   [Google Scholar]     
  5. Spickerman WR (1970). A note on fibonacci functions. The Fibonacci Quarterly, 8(4): 397-401.   [Google Scholar]     
  6. Sroysang B (2013). On fibonacci functions with period. Discrete Dynamics in Nature and Society, 2013: Article ID 418123, 4 pages.   [Google Scholar]