5: Convergence of the Taylor Series- A “Tayl” of Three Remainders — Read

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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.
5.E: Convergence of the Taylor Series- A “Tayl” of Three Remainders (Exercises)

Thumbnail: Brook Taylor (1685-1731) was an English mathematician who is best known for Taylor's theorem and the Taylor series.

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