Euler’s constant, new classes of sequences and estimates

We give two classes of sequences with the argument of the logarithmic term modified and also with some additional terms besides those in the denition sequence, and that converge quickly to <img src="http:/fbpe/img/cubo/v15n3/art10-fig1.jpg" name="_x0000_i1043" width=380 height...

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Autor principal:	Sîntămărian,Alina
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2013
Materias:	sequence convergence approximation Euler’s constant Bernoulli number estimate
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000300010
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spelling	oai:scielo:S0719-064620130003000102018-10-08Euler’s constant, new classes of sequences and estimatesSîntămărian,Alina sequence convergence approximation Euler’s constant Bernoulli number estimate We give two classes of sequences with the argument of the logarithmic term modified and also with some additional terms besides those in the denition sequence, and that converge quickly to <img src="http:/fbpe/img/cubo/v15n3/art10-fig1.jpg" name="_x0000_i1043" width=380 height=40 border=0 id="_x0000_i1043">, where a <img src="http:/fbpe/img/cubo/v15n3/art05-fig7.jpg" name="_x0000_i1042" width=17 height=17 border=0 id="_x0000_i1042"> (0, + <img src="http:/fbpe/img/cubo/v15n3/art10-fig7.jpg" name="_x0000_i1041" width=18 height=13 border=0 id="_x0000_i1041">). We present the pattern in forming these sequences, expressing the coefficients that appear with the Bernoulli numbers. Also, we obtain estimates containing best constants for <img src="http:/fbpe/img/cubo/v15n3/art10-fig2.jpg" name="_x0000_i1040" width=507 height=41 border=0 id="_x0000_i1040">and <img src="http:/fbpe/img/cubo/v15n3/art10-fig3.jpg" name="_x0000_i1039" width=38 height=28 border=0 id="_x0000_i1039"><img src="http:/fbpe/img/cubo/v15n3/art10-fig4.jpg" name="_x0000_i1038" width=600 height=38 border=0 id="_x0000_i1038">, where <img src="http:/fbpe/img/cubo/v15n3/art10-fig5.jpg" name="_x0000_i1037" width=19 height=23 border=0 id="_x0000_i1037"> = <img src="http:/fbpe/img/cubo/v15n3/art10-fig5.jpg" name="_x0000_i1036" width=19 height=23 border=0 id="_x0000_i1036">(1) is the Euler’s onstant.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.15 n.3 20132013-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000300010en10.4067/S0719-06462013000300010
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	sequence convergence approximation Euler’s constant Bernoulli number estimate
spellingShingle	sequence convergence approximation Euler’s constant Bernoulli number estimate Sîntămărian,Alina Euler’s constant, new classes of sequences and estimates
description	We give two classes of sequences with the argument of the logarithmic term modified and also with some additional terms besides those in the denition sequence, and that converge quickly to <img src="http:/fbpe/img/cubo/v15n3/art10-fig1.jpg" name="_x0000_i1043" width=380 height=40 border=0 id="_x0000_i1043">, where a <img src="http:/fbpe/img/cubo/v15n3/art05-fig7.jpg" name="_x0000_i1042" width=17 height=17 border=0 id="_x0000_i1042"> (0, + <img src="http:/fbpe/img/cubo/v15n3/art10-fig7.jpg" name="_x0000_i1041" width=18 height=13 border=0 id="_x0000_i1041">). We present the pattern in forming these sequences, expressing the coefficients that appear with the Bernoulli numbers. Also, we obtain estimates containing best constants for <img src="http:/fbpe/img/cubo/v15n3/art10-fig2.jpg" name="_x0000_i1040" width=507 height=41 border=0 id="_x0000_i1040">and <img src="http:/fbpe/img/cubo/v15n3/art10-fig3.jpg" name="_x0000_i1039" width=38 height=28 border=0 id="_x0000_i1039"><img src="http:/fbpe/img/cubo/v15n3/art10-fig4.jpg" name="_x0000_i1038" width=600 height=38 border=0 id="_x0000_i1038">, where <img src="http:/fbpe/img/cubo/v15n3/art10-fig5.jpg" name="_x0000_i1037" width=19 height=23 border=0 id="_x0000_i1037"> = <img src="http:/fbpe/img/cubo/v15n3/art10-fig5.jpg" name="_x0000_i1036" width=19 height=23 border=0 id="_x0000_i1036">(1) is the Euler’s onstant.
author	Sîntămărian,Alina
author_facet	Sîntămărian,Alina
author_sort	Sîntămărian,Alina
title	Euler’s constant, new classes of sequences and estimates
title_short	Euler’s constant, new classes of sequences and estimates
title_full	Euler’s constant, new classes of sequences and estimates
title_fullStr	Euler’s constant, new classes of sequences and estimates
title_full_unstemmed	Euler’s constant, new classes of sequences and estimates
title_sort	euler’s constant, new classes of sequences and estimates
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2013
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000300010
work_keys_str_mv	AT sint259m259rianalina eulerrsquosconstantnewclassesofsequencesandestimates
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Euler&rsquo;s constant, new classes of sequences and estimates

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