Why was Taylor series around zero named Maclaurin series?

Question

I am eager to know why was Maclaurin series ,which is a special case of Taylor series, named after Taylor's finding?

I myself guessed that Maclaurin found his series for functions around zero, and then Taylor expanded that series for the other points; but, after googling the history of Maclaurin series, I found out that Maclaurin used Taylor series.

So, my question is that what is the importance of Maclaurin's work so that Taylor series around zero named Maclaurin series?

Answer 1

See Colin Maclaurin (1698-1746) and Brook Taylor (1685-1731):

Maclaurin in the Treatise of fluxions: In Two Books (1742) uses the special case of Taylor series [though it would only be known as this in 1785] now named after him and for which he is undoubtedly best remembered today. The Maclaurin series was not an idea discovered independently of the more general result of Taylor for Maclaurin acknowledges Taylor's contribution.

Maclaurin (Book Two, page 611) credits Taylor's Methodus incrementorum (1717; 1st ed 1715), see COROLL.II, page 23.

We have to consider the relevance of Maclaurin's Treatise: it was the first "textbook" dedicated to the fluxional calculus; see:

• Judith Grabiner, Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions, The American Mathematical Monthly (1997).

According to Grabiner, "the result Maclaurin himself credited to Taylor, and it was known earlier to Newton and Gregory",

was called the Maclaurin series by John F.W. Herschel, Charles Babbage, and George Peacock in 1816 [in their English transaltion of Silvestre François Lacroix's treatise: An Elementary Treatise on the Differential and Integral Calculus (French first ed., 1797-1800), see Note (C), page 620-21, referred into page 24, and written by George Peacock] and by Cauchy in 1823. [Résumé des leçons sur le calcul infinitésimal (1823),page 147].

But the link Taylor-Maclaurin was already noted by Lacroix himself at least in the 2nd French edition of his Traité (1810), see page xxvii of the Préface.

As you can see, the history of "naming" is not always linear...