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=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.
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2013
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000300010 |
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