Notes on Euler’swork on divergent factorial series and their associated continued fractions

Autor:	Trond Digernes, Veeravalli S. Varadarajan
Rok vydání:	2010
Předmět:	Algebra Factorial symbols.namesake Series (mathematics) Applied Mathematics General Mathematics Numerical analysis Euler's formula symbols Divergent series Borel summation Mathematics
Zdroj:	Indian Journal of Pure and Applied Mathematics. 41:39-66
ISSN:	0975-7465 0019-5588
DOI:	10.1007/s13226-010-0019-8
Popis:	Factorial series which diverge everywhere were first considered by Euler from the point of view of summing divergent series. He discovered a way to sum such series and was led to certain integrals and continued fractions. His method of summation was essentialy what we call Borel summation now. In this paper, we discuss these aspects of Euler’s work from the modern perspective.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::beb4fd84e908b80a8f92d7207b9a3b63 https://doi.org/10.1007/s13226-010-0019-8 Zobrazit plný text záznamu Full text from SpringerLink