- 5.1: The Integral Form of the Remainder
- Now that we have a rigorous deﬁnition of the convergence of a sequence, let’s apply this to Taylor series.
- 5.2: Lagrange’s Form of the Remainder
- Joseph-Louis Lagrange provided an alternate form for the remainder in Taylor series in his 1797 work Théorie des functions analytiques.
- 5.3: Cauchy’s Form of the Remainder
- In his 1823 work, Résumé des le¸cons données à l’ecole royale polytechnique sur le calcul inﬁntésimal, Augustin Cauchy provided another form of the remainder for Taylor series.
Thumbnail: Brook Taylor (1685-1731) was an English mathematician who is best known for Taylor's theorem and the Taylor series.
Eugene Boman (Pennsylvania State University) and Robert Rogers (SUNY Fredonia)