Joseph Ser (1875–1954) was a

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

mathematician, of whom little was known till now. He published 45 papers between 1900 and 1954, among which four monographs, edited in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

Henry Gauthier-Villars Henry Gauthier-Villars (8 August 1859 – 12 January 1931), known by the pen name Willy , was a French ''fin de siècle'' writer and music critic who is today mostly known as the mentor and first husband of Colette. Other pseudonyms used by Gauth ...

. In the main, he worked on

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and

infinite series In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, math ...

. He got important results in the domain of

factorial In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \t ...

series. His representation of

Euler's constant Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural ...

as a series of

rational Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abili ...

terms is well known. It was used in 1926 by

Paul Appell Paul may refer to: *Paul (given name), a given name (includes a list of people with that name) *Paul (surname), a list of people People Christianity * Paul the Apostle (AD c.5–c.64/65), also known as Saul of Tarsus or Saint Paul, early Chri ...

(1855–1930), in an unsuccessful attempt to prove the irrationality of Euler's constant.

References

* Ser, Joseph : ''Sur une expression de la fonction ζ(s) de Riemann (Upon an expression for Riemann's ζ function)''. CRAS (Paris) vol.182(1926),1075-1077 *Ayoub, Raymond G.: ''Partial triumph or total failure ?'' The mathematical Intelligencer, vol.7, No 2(1985),55-58. This paper explains exactly Appell's mistake (4 - Appell and the irrationality of Euler's constant). {{DEFAULTSORT:Ser, Joseph French mathematicians 1875 births 1954 deaths