Taylor polynomial

• Taylor's polynomial

Taylor polynomial (plural Taylor polynomials)

1. (mathematical analysis) A truncated Taylor series; the sum of the first n terms of a Taylor series.
   • 1980, Donald W. Kahn, Introduction to Global Analysis, Academic Press, page 314:

     For example, if ${\displaystyle M^{n}=\mathbb {R} ^{n}}$ and ${\displaystyle N^{k}=\mathbb {R} }$, a singularity means the vanishing of the gradient, or equivalently, the linear terms of the Taylor's polynomial of some degree greater than 1. If one has a singularity, one may look at the second-order terms in the Taylor's polynomial.

   • 1989, J. Berry, John Stephen Berry, A. Norcliffe, S. Humble, Introductory Mathematics Through Science Applications, Cambridge University Press, page 211:

     The polynomial approximation above for exp(x) is an example of a Taylor polynomial of degree 2 and in fact the polynomial approximations to sin(x) and cos(x) that we wrote down in Chapter 3 are also Taylor polynomials.

   • 2007, Andrea Bonfiglioli, Ermanno Lanconelli, Francesco Uguzzoni, Stratified Lie Groups and Potential Theory for their Sub-Laplacians, Springer, page 733:

     Then, we introduce and investigate the Taylor polynomials and we prove suitable versions of the Lagrange mean value theorem and of the Taylor formula.

• Maclaurin polynomial