Abstract
van der Corput's inequality is extended and refined by using Euler-Maclaurin formula and other analytic techniques.
van der Corput's inequality is extended and refined by using Euler-Maclaurin formula and other analytic techniques.
G. E. Andrews, R. Askey, and R. Roy, Special Functions, vol. 71 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 1999.
View at: Zentralblatt MATH | MathSciNetB. Autora, “Publication list: J. G. van der Corput,” Acta Arithmetica, vol. 36, no. 1, pp. 91–99, 1980.
View at: Google Scholar | MathSciNetCh.-P. Chen and F. Qi, “On further sharpening of Carleman's inequality,” Dàxué Shùxué (College Mathematics), vol. 21, no. 2, pp. 88–90, 2005 (Chinese).
View at: Google ScholarA. Z. Grinshpan and M. E. H. Ismail, “Completely monotonic functions involving the gamma and -gamma functions,” Proceedings of the American Mathematical Society, vol. 134, no. 4, pp. 1153–1160, 2006.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Hu, “On the van der Corput inequality,” Journal of Mathematics (Shùxué Zázhì), vol. 23, no. 1, pp. 126–128, 2003 (Chinese).
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ.-Ch. Kuang, “Asymptoic estimations of finite sums,” Journal of Hexi University, vol. 2, no. 2, pp. 1–8, 2002 (Chinese).
View at: Google ScholarF. Qi, “Certain logarithmically -alternating monotonic functions involving gamma and -gamma functions,” RGMIA Research Report Collection, vol. 8, no. 3, 2005, article 5, available online at http://rgmia.vu.edu.au/v8n3.html.
View at: Google ScholarF. Qi and B.-N. Guo, “Complete monotonicities of functions involving the gamma and digamma functions,” RGMIA Research Report Collection, vol. 7, no. 1, pp. 63–72, 2004, article 8, available online at http://rgmia.vu.edu.au/v7n3.html.
View at: Google ScholarF. Qi, B.-N. Guo, and C.-P. Chen, “Some completely monotonic functions involving the gamma and polygamma functions,” Journal of the Australian Mathematical Society, vol. 80, no. 1, pp. 81–88, 2006, RGMIA Research Report Collection 7 (2004), no. 1, 31–36, article 5, available online at http://rgmia.vu.edu.au/v7n1.html.
View at: Google Scholar | MathSciNetJ. G. van der Corput, “Generalization of Carleman's inequality,” Proceedings of the Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam, vol. 39, pp. 906–911, 1936.
View at: Google ScholarH. van Haeringen, “Completely monotonic and related functions,” Report 93-108, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, 1993.
View at: Google ScholarB.-Ch. Yang, “On a strengthened version of the more precise Hardy-Hilbert inequality,” Acta Mathematica Sinica, vol. 42, no. 6, pp. 1103–1110, 1999 (Chinese).
View at: Google Scholar | Zentralblatt MATH | MathSciNetB.-Ch. Yang, “On Hardy's inequality,” Journal of Mathematical Analysis and Applications, vol. 234, no. 2, pp. 717–722, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetB.-Ch. Yang, “On a relation between Carleman's inequality and Van der Corput's inequality,” Taiwanese Journal of Mathematics, vol. 9, no. 1, pp. 143–150, 2005.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB.-Ch. Yang, “On an extension and a refinement of van der Corput's inequality,” to appear in Chinese Quarterly Journal of Mathematics.
View at: Google Scholar