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Euler's beta integral in Pietro Mengoli's works
dc.contributor.author | Massa Esteve, Maria Rosa |
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2011-01-18T11:31:46Z |
dc.date.available | 2011-01-18T11:31:46Z |
dc.date.created | 2009-03 |
dc.date.issued | 2009-03 |
dc.identifier.citation | Massa, M.; Delshams, A. Euler's beta integral in Pietro Mengoli's works. "Archive for history of exact sciences", Març 2009, vol. 63, núm. 3, p. 325-356. |
dc.identifier.issn | 0003-9519 |
dc.identifier.uri | http://hdl.handle.net/2117/11075 |
dc.description.abstract | Beta integrals for several non-integer values of the exponents were calculated by Leonhard Euler in 1730, when he was trying to find the general term for the factorial function by means of an algebraic expression. Nevertheless, 70 years before, Pietro Mengoli (1626–1686) had computed such integrals for natural and half-integer exponents in his Geometriae Speciosae Elementa (1659) and Circolo (1672) and displayed the results in triangular tables. In particular, his new arithmetic–algebraic method allowed him to compute the quadrature of the circle. The aim of this article is to show how Mengoli calculated the values of these integrals as well as how he analysed the relation between these values and the exponents inside the integrals. This analysis provides new insights into Mengoli’s view of his algorithmic computation of quadratures. |
dc.format.extent | 32 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Mengoli, Pietro, 1625-1686 |
dc.subject.lcsh | Euler, Leonhard, 1707-1783. |
dc.subject.lcsh | Arithmetical algebraic geometry. |
dc.title | Euler's beta integral in Pietro Mengoli's works |
dc.type | Article |
dc.subject.lemac | Mengoli, Pietro |
dc.subject.lemac | Euler, Leonhard, 1707-1783 |
dc.subject.lemac | Geometria algebraica aritmètica |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.contributor.group | Universitat Politècnica de Catalunya. GRHCT - Grup de Recerca d'Història de la Ciència i de la Tècnica |
dc.identifier.doi | 10.1007/s00407-009-0042-5 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://www.springerlink.com/content/gu0g264614228416/fulltext.pdf |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 739138 |
dc.description.version | Postprint (published version) |
local.citation.author | Massa, M.; Delshams, A. |
local.citation.publicationName | Archive for history of exact sciences |
local.citation.volume | 63 |
local.citation.number | 3 |
local.citation.startingPage | 325 |
local.citation.endingPage | 356 |
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