"What's
in
a name? That which we call a rose

By any other name would smell as sweet."

Romeo and Juliet (II, ii, 1-2)

Taylor's Theorem was stated in 1712 by Brook Taylor
(1685-1731), forty one years __ after__ it was originally
announced in 1671 by James Gregory (1638-1675). And special
cases were already known by Madhava of Sanyamagrama (1350-1425).

Of course Colin Maclaurin (1698-1746) did __ not__ discover
the Maclaurin series. He discovered the integral test for the
convergence of infinite series.

Gabriel Cramer (1704-1752) published Cramer's rule two
years __after__ it was published by Colin Maclaurin.

Stokes' Theorem was __ not__ discovered by Gabriel Stokes
(1819-1903) at all. It was discovered by William Thomson, a.k.a.
Lord Kelvin (1824-1907).

[*In fact my friend Okan Tekman informed me that this theorem
has a longer and more convoluted history. See
Okan's
summary.*]

Stirling's formula was __ not__ discovered by James
Stirling (1692-1770) but was discovered by Abraham de Moivre
(1667-1754).

**So, before the historians come in, here is Sertoz
Theorem: **

For a proof of the theorem,
follow this link. (**New:**
An alternate proof is added which uses the Lagrange multipliers
method, after an idea of Murad Özaydın.)

**Türkçe'si için buraya
tıklayabilirsiniz.**

---Here is an application:

Here is the answer:

(3/4)+(2/12)+(1/14) = (83/84) < 1, so the first limit does not exist, but (3/4)+(2/12)+(2/14) = (89/84) > 1, so the second limit exists and is zero.

---

It should be added that the L'hospital's rule was not discovered by Guillaume L'Hospital (1661-1704) but was a theorem of Johann Bernoulli (1667-1748).

Recently there is some work to generalize L'Hospital's rule to multivariate case.

See for example Gary R. Lawlor and V. V. Ivlev and I. A. Shilin.

(