# Traian Lalescu

Traian Lalescu (Romanian: [traˈjan laˈlesku]; 12 July 1882 – 15 June 1929) was a Romanian mathematician. His main focus was on integral equations and he contributed to work in the areas of functional equations, trigonometric series, mathematical physics, geometry, mechanics, algebra, and the history of mathematics.

Traian Lalescu
Born12 July 1882
Died15 June 1929 (aged 46)
ResidenceRomania
NationalityRomanian
Alma materUniversity of Bucharest
University of Paris
Known forIntegral equations
Scientific career
FieldsMathematician
InstitutionsPolytechnic University of Timișoara
University of Bucharest

## Life

He went to the Carol I High School in Craiova, continuing high school in Roman, and graduating from the Boarding High School in Iași. After entering the University of Iași, he completed his undergraduate studies in 1903 at the University of Bucharest.

He earned his Ph.D. in Mathematics from the University of Paris in 1908. His dissertation, Sur les équations de Volterra, was written under the direction of Émile Picard. In 1911, he published Introduction to the Theory of Integral Equations, the first book ever on the subject of integral equations.

He was a professor at the University of Bucharest, the Polytechnic University of Timișoara (where he was the first rector, in 1920), and the Polytechnic University of Bucharest.

## The Lalescu sequence

${\displaystyle L_{n}={\sqrt[{n+1}]{(n+1)!}}-{\sqrt[{n}]{n!}}}$
${\displaystyle \lim _{n\to \infty }L_{n}={\frac {1}{e}}}$

## Legacy

There are several institutions bearing his name, including Colegiul Naţional de Informatică Traian Lalescu in Hunedoara and Liceul Teoretic Traian Lalescu in Reşiţa. There is also a Traian Lalescu Street in Timişoara. The National Mathematics Contest Traian Lalescu for undergraduate students is also named after him.

A statue of Lalescu, carved in 1930 by Cornel Medrea, is situated in front of the Faculty of Mechanical Engineering, in Timişoara.

## Work

• T. Lalesco, Introduction à la théorie des équations intégrales. Avec une préface de É. Picard, Paris: A. Hermann et Fils, 1912. VII + 152 pp.[1] JFM entry
• Traian Lalescu, Introducere la teoria ecuaţiilor integrale, Editura Academiei Republicii Populare Romîne, 1956. 134 pp. (A reprint of the first edition [Bucharest, 1911], with a bibliography taken from the French translation [Paris, 1912]). MR0085450

## References

1. ^ Longley, W. R. (1913). "Review: Introduction à la Théorie des Équations intégrales by T. Lalesco and L'Équation de Fredholm et ses Applications à la Physique mathématique by H. B. Heywood and M. Frechét". Bull. Amer. Math. Soc. 19: 236–241. doi:10.1090/S0002-9904-1913-02333-4.