A polynomial approximation for arbitrary functions

Citations of this article
Mendeley users who have this article in their library.


We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, for approximating arbitrary functions. We show that the polynomial coefficients in the Legendre expansion, and thus, the whole series, converge to zero much more rapidly compared to those in the Taylor expansion of the same order. Furthermore, using numerical analysis with a sixth-order polynomial expansion, we demonstrate that the Legendre polynomial approximation yields an error at least an order of magnitude smaller than that of the analogous Taylor series approximation. This strongly suggests that Legendre expansions, instead of Taylor expansions, should be used when global accuracy is important. © 2012 Elsevier Ltd.




Cohena, M. A., & Tan, C. O. (2012). A polynomial approximation for arbitrary functions. Applied Mathematics Letters, 25(11), 1947–1952. https://doi.org/10.1016/j.aml.2012.03.007

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free