Geodesic
A Refinement of the Becker--Stark Inequalities
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 401-406.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a refinement of the Becker–Stark inequalities is established and a simple proof of this new inequality is given.
Keywords: Bernoulli numbers, Riemann's zeta function, power series expansion, upper and lower bounds, Becker–Stark inequalities. 
@article{MZM_2013_93_3_a7,
     author = {Ling Zhu},
     title = {A {Refinement} of the {Becker--Stark} {Inequalities}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {401--406},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a7/}
}
TY  - JOUR
AU  - Ling Zhu
TI  - A Refinement of the Becker--Stark Inequalities
JO  - Matematičeskie zametki
PY  - 2013
SP  - 401
EP  - 406
VL  - 93
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a7/
LA  - ru
ID  - MZM_2013_93_3_a7
ER  - 
%0 Journal Article
%A Ling Zhu
%T A Refinement of the Becker--Stark Inequalities
%J Matematičeskie zametki
%D 2013
%P 401-406
%V 93
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a7/
%G ru
%F MZM_2013_93_3_a7
Ling Zhu. A Refinement of the Becker--Stark Inequalities. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 401-406. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a7/

[1] S. B. Stechkin, “Neskolko zamechanii o trigonometricheskikh polinomakh”, UMN, 10:1 (1955), 159–166 | MR | Zbl

[2] D. S. Mitrinović, Analytic Inequalities, Grundlehren Math. Wiss., 165, Springer-Verlag, Berlin, Heidelberg, New York, 1970 | MR | Zbl

[3] M. Becker, E. L. Stark, “On hierarchy of polynomial inequalities for $\operatorname{tan}(x)$”, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 602–633 (1978), 133–138 | MR | Zbl

[4] J. C. Kuang, Applied Inequalities, Shangdong Sci. Tech. Press, Jinan City, Shangdong Province, China, 2004 (Chinese)

[5] G. D. Anderson, S.-L. Qiu, M. K. Vamanamurthy, M. Vuorinen, “Generalized elliptic integral and modular equations”, Pacific J. Math., 192:1 (2000), 1–37 | DOI | MR | Zbl

[6] G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, “Inequalities for quasiconformal maps in space”, Pacific J. Math., 160:1 (1993), 1–18 | MR | Zbl

[7] I. Pinelis, “L'Hospital rules for monotonicity and the Wilker–Anglesio inequality”, Amer. Math. Monthly, 111:10 (2004), 905–909 | DOI | MR | Zbl

[8] A. Jeffrey, Handbook of Mathematical Formulas and Integrals, Elsevier Acad. Press, San Diego, CA, 2004 | MR | Zbl

[9] K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Grad. Texts in Math., 84, Springer-Verlag, New York, 1990 | MR | Zbl

[10] W. Scharlau, H. Opolka, From Fermat to Minkowski. Lectures on the Theory of Numbers and its Historical Development, Undergrad. Texts Math., Springer-Verlag, New York, 1985 | MR | Zbl

[11] C.-P. Chen, F. Qi, “A double inequality for remainder of power series of tangent function”, Tamkang J. Math., 34:4 (2003), 351–355 | MR | Zbl