Document Type : Research Paper


Department of Mathematics, University of Farhangian, Tehran, Iran.


In this paper, a class of new polynomials based on Fibonacci sequence using Newton interpolation is introduced. This target is performed once using Newton forward- divided- difference formula and another more using Newton backward- divided- difference formula. Some interesting results are obtained for forward and backward differences. The relationship between forward (and backward) differences and the Khayyam- Pascal's triangle are also examined.


[1] T. Amdeberhan, X. Chen, V. Moll and B. Sagan, Generalized Fibonacci polynomials and fibonomial coefficients, Ann. Comb., 18 (2014), pp. 541-562.
[2] S. Bazm, Numerical solution of a class of nonlinear two-dimensional integral equations using Bernoulli polynomials, Sahand Commun. Math. Anal., 3 (1) (2016), pp. 37-51
[3] R.L. Burden, J.D. Faires and A.M. Burden, Numerical Analysis, Tenth edition, Cengage Learning, Boston, Massachusetts, 2016.
[4] D. Garth, D. Mills and P. Mitchell, Polynomials generated by the Fibonacci sequence, J. Integer Seq., 10 (2007), Article 07.6.8.
[5] B. Hamza, A. Chafik and T. Mohamed, Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations, Sahand Commun. Math. Anal., 20 (1) (2023), pp. 45-60
[6] D. Kincaid and W. Cheney, Numerical Analysis Mathematics of Scientific Computing, Third Edition., AMS., 2017.
[7] M.S. Mufid, T. Asfihani and L. Hanaf,On The Lagrange Interpolation of Fibonacci Sequence, IJCSAM., 2 (2016), pp. 38-40.
[8] T. Scott and P. Marketos,On the origin of Fibonacci sequence, MacTutor History of Mathematics, University of St Andrews, Scotland, 2014.