Skip to main content

Free Content When Euler Met l'Hôpital

Download Article:
(PDF 459.7 kb)


In the fifteenth chapter of his 1755 text on differential calculus, Leonhard Euler considered indeterminate expressions of the form 0/0 and provided a string of dazzling examples that make modern treatments of the subject look quite pedestrian. Some indeterminate forms he evaluated with basic algebra, some with trigonometric identities, and some with infinite series. And, as the title suggests, he rolled out the heavy artillery of l'Hospital's rule. In Euler's hands, this served not just to solve specially-concocted problems but to evaluate the sum of the first n whole numbers. More improbably, he applied l'Hospital's rule (three times!) to resolve the Basel problem, i.e., to sum the infinite series of the reciprocals of the squares. By examining these results, we hope to reveal a master at work.

Document Type: Research Article


Publication date: February 1, 2009

More about this publication?

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more