000064311 001__ 64311 000064311 005__ 20210121114506.0 000064311 0247_ $$2doi$$a10.4169/amer.math.monthly.122.5.444 000064311 0248_ $$2sideral$$a102743 000064311 037__ $$aART-2015-102743 000064311 041__ $$aeng 000064311 100__ $$aCiaurri, Óscar 000064311 245__ $$aA simple computation of Z(2k) 000064311 260__ $$c2015 000064311 5060_ $$aAccess copy available to the general public$$fUnrestricted 000064311 5203_ $$aWe present a new simple proof of Euler’s formulas for Z(2k), where k= 1,2,3,.... The computation is done using only the defining properties of the Bernoulli polynomials and summing a telescoping series, and the same method also yields integral formulas for Z(2k+ 1). 000064311 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-36732-C03-02 000064311 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000064311 590__ $$a0.349$$b2015 000064311 591__ $$aMATHEMATICS$$b273 / 312 = 0.875$$c2015$$dQ4$$eT3 000064311 592__ $$a0.408$$b2015 000064311 593__ $$aMathematics (miscellaneous)$$c2015$$dQ3 000064311 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000064311 700__ $$aNavas, Luis M. 000064311 700__ $$0(orcid)0000-0001-5364-4799$$aRuiz Blasco, Francisco J.$$uUniversidad de Zaragoza 000064311 700__ $$aVarona, Juan L. 000064311 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000064311 773__ $$g122, 5 (2015), 444-451$$pAm. math. mon.$$tAmerican Mathematical Monthly$$x0002-9890 000064311 8564_ $$s225079$$uhttps://zaguan.unizar.es/record/64311/files/texto_completo.pdf$$yPostprint 000064311 8564_ $$s54422$$uhttps://zaguan.unizar.es/record/64311/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000064311 909CO $$ooai:zaguan.unizar.es:64311$$particulos$$pdriver 000064311 951__ $$a2021-01-21-10:54:24 000064311 980__ $$aARTICLE