# Why does Maclaurin get his own polynomial?

Why is a Taylor polynomial centered around $0$ called a Maclaurin polynomial? It's only a special case of the Taylor polynomial, and it is calculated the exact same way as a Taylor polynomial centered at any number. It doesn't seem to carry the same weight as other named concepts such as Euler's number, which has special properties when you differentiate, integrate, etc.

• I might be wrong, but from (very old) memory, didn't Maclaurin discover his series expansion first (so it was known as the Maclaurin expansion from then on) and then at a later date, Taylor came along and discovered a more general version ... called the Taylor expansion? – Old John Jul 18 '12 at 23:51
• Good grief - it WAS the other way round. How amazing. – Old John Jul 18 '12 at 23:58
• Ah, didn't think to check his biography as well. That still doesn't explain why a special case is named after him. It wasn't a new discovery or anything, it was just a specific case of something already discovered that helped him figure out other things. – Nick Anderegg Jul 18 '12 at 23:58
• And Taylor series were used in Kerala by the fourteenth century. But who said the European namers of things have to be fair? – André Nicolas Jul 19 '12 at 0:10
• The Madhava (माधव) series, maybe? Perhaps in future they will be known as the Apple (maybe Samsung) series (with appropriate trademarks, etc.)? – copper.hat Jul 19 '12 at 7:16

Stigler's Law: No scientific discovery is named after its original discoverer (this was discovered by Merton).

• Taylor got credit though. I don't understand why Maclaurin gets credits for using a special case. It's not a new discovery, it's just a tool. – Nick Anderegg Jul 18 '12 at 23:59
• e.g. Pell's equation was so-called because Pell had nothing to do with it? :) – Old John Jul 18 '12 at 23:59
• @NickAnderegg Why bother that much? I mean, it isn't like you can go and complain at him - I mean, I don't like it either than Mascheroni got his name in Euler's constant, after even miscalculating it: I just call it Euler's constant. You can just call them Taylor series to honor him. – Pedro Tamaroff Jul 19 '12 at 0:01
• @OldJohn It is called Pell equation because Euler mistook him for another mathematician who was the one that studied it and found algorithms to solve it when writing a letter to Goldbach. How ironic, I don't even remember his name. – Pedro Tamaroff Jul 19 '12 at 0:01
• Lord Brouncker, I believe. – Old John Jul 19 '12 at 0:03

It's called a Maclaurin series because Colin Maclaurin made extensive use of them to make advancements in the field of geometry. He also covered this case of Taylor series extensively in his treatise of fluxions.

If you want a really unfair example, you should see l'Hôpital's rule. This rule was discovered by Johann Bernoulli but it is named l'Hôpital's rule because a guy called Guillaume de l'Hôpital published it in his book on differential calculus.

• Be fair: L'hopital paid Bernoulli for the right to publish the rule in the former's textbook. As someone said, "Let the good Marquis keep his rule; after all, he paid for it fair and square." – Arturo Magidin Jul 18 '12 at 23:59
• Hey, at least Taylor got credit for originally coming up with it. I'm familiar with the history L'hopital's rule, and I kind of wish Bernoulli got credit just because it would probably be easier for my heavily-accented calculus professor to say. – Nick Anderegg Jul 19 '12 at 0:00
• I think its fair to Johann Bernoulli, but someone would probably not be able to do that nowadays. – Jorge Fernández Hidalgo Jul 19 '12 at 0:01
• @ArturoMagidin That's why I call it Bernoulli-L'Hôpital whenever I remember. – Pedro Tamaroff Jul 19 '12 at 0:03
• @ChuckFernandez: And L'Hopital gave appropriate recognition to Bernoulli (at least from the second edition onwards). My understanding is that it was originally refered to by the longer but more accurate "Rule in L'Hopital's book" or some such. In any case, there are lots of things that you would not be able to do today that were pretty common back then, and has nothing to do with fairness of unfairness. On a separate note, don't use accent graves, use apostrophes. Accent graves are special characters for the parser. – Arturo Magidin Jul 19 '12 at 0:05