Name this person whose namesake polynomials, a specific case of which are MacLaurin series, use derivatives and factorials to approximate a function.
Some versions of the theorem named for this person have the Radius of Convergence Theorem built into them. His namesake theorem applies to functions that are smooth at x=0. Additionally, some versions have a term attributed to Lagrange [lah-GRANJ] or Cauchy [cow-shee] to account for errors. His theorem develops polynomials from repeatedly differentiable functions. Name this person whose namesake polynomials, a specific case of which are MacLaurin series, use derivatives and factorials to approximate a function.
Some versions of the theorem named for this person have the Radius of Convergence Theorem built into them.
Brook Taylor