In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-9
Kurzfassung:
We prove that p = 1 and q = 2 are the best possible parameters in the interval ( 0 , ∞ ) such that the double inequality e p / x + 1 - e - p / x / 2 p 〈 ψ ′ x + 1 〈 e q / x + 1 - e - q / x / 2 q holds for x 〉 0 . As applications, some new approximation algorithms for the circumference ratio π and Catalan constant G = ∑ n = 0 ∞ - 1 n / ( 2 n + 1 ) 2 are given. Here, ψ ′ is the trigamma function.
Materialart:
Online-Ressource
ISSN:
1085-3375
,
1687-0409
Sprache:
Englisch
Verlag:
Hindawi Limited
Publikationsdatum:
2014
ZDB Id:
2064801-7
SSG:
17,1
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