메뉴 건너뛰기




Volumn 133, Issue 2, 2005, Pages 397-401

The best bounds in wallis' inequality

Author keywords

Best bound; Gamma function; Monotonicity; Wallis' inequality

Indexed keywords


EID: 13544261733     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-04-07499-4     Document Type: Conference Paper
Times cited : (67)

References (23)
  • 1
    • 0003312531 scopus 로고
    • Handbook of mathematical functions with formulas, graphs, and mathematical tables
    • National Bureau of Standards, 9th printing, Dover, New York. MR 34:8607
    • M. Abramowitz and I. A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, 9th printing, Dover, New York, 1972. MR 34:8607
    • (1972) Applied Mathematics Series , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 0042376839 scopus 로고    scopus 로고
    • On some inequalities for the gamma and psi functions
    • MR 97e:33004
    • H. Alzer, On some inequalities for the gamma and psi functions, Math. Comp. 66 (1997), 373-389. MR 97e:33004
    • (1997) Math. Comp. , vol.66 , pp. 373-389
    • Alzer, H.1
  • 5
    • 13544265686 scopus 로고    scopus 로고
    • Improvement of lower bound in Wallis' inequality
    • Art. 23
    • Ch.-P. Chen and F. Qi, Improvement of lower bound in Wallis' inequality, RGMIA Res. Rep. Coll. 5 (2002), suppl., Art. 23. Available online at http://rgmia.vu.edu.au/v5(E).html.
    • (2002) RGMIA Res. Rep. Coll. , vol.5 , Issue.SUPPL.
    • Chen, Ch.-P.1    Qi, F.2
  • 6
    • 13844265351 scopus 로고    scopus 로고
    • The best bounds in Wallis' inequality
    • Art. 13
    • Ch.-P. Chen and F. Qi, The best bounds in Wallis' inequality, RGMIA Res. Rep. Coll. 5 (2002), no. 4, Art. 13. Available online at http://rgmia.vu.edu.au/v5n4.html.
    • (2002) RGMIA Res. Rep. Coll. , vol.5 , Issue.4
    • Chen, Ch.-P.1    Qi, F.2
  • 7
    • 13544251755 scopus 로고    scopus 로고
    • A new proof of the best bounds in Wallis' inequality
    • Art. 2
    • Ch.-P. Chen and F. Qi, A new proof of the best bounds in Wallis' inequality, RGMIA Res. Rep. Coll. 6 (2003), no. 2, Art. 2. Available online at http://rgmia.vu.edu.au/v6n2.html.
    • (2003) RGMIA Res. Rep. Coll. , vol.6 , Issue.2
    • Chen, Ch.-P.1    Qi, F.2
  • 8
    • 13544259985 scopus 로고    scopus 로고
    • Archimedes' constant, § 1.4
    • Cambridge Univ. Press, Cambridge, England
    • S. R. Finch, Archimedes' Constant, § 1.4 in Mathematical Constants, Cambridge Univ. Press, Cambridge, England, 2003. Available online at http://pauillac.inria.fr/algo/bsolve/.
    • (2003) Mathematical Constants
    • Finch, S.R.1
  • 9
    • 0001160530 scopus 로고
    • Error bounds for asymptotic expansions of the ratio of two gamma functions
    • MR 88d:33001
    • C. L. Frenzer, Error bounds for asymptotic expansions of the ratio of two gamma functions, SIAM J. Math. Anal. 18 (1987), 890-896. MR 88d:33001
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 890-896
    • Frenzer, C.L.1
  • 10
    • 13544255771 scopus 로고    scopus 로고
    • http://mathworld.wolfram.com/HadamardProduct.html.
  • 11
    • 13544269634 scopus 로고    scopus 로고
    • http://mathworld.wolfram.com/RiemannZetaFunction.html.
  • 12
    • 13544263615 scopus 로고    scopus 로고
    • http://mathworld.wolfram.com/WallisFormula.html.
  • 13
    • 13544261777 scopus 로고    scopus 로고
    • http://mathworld.wolfram.com/WallisCosineFormula.html.
  • 14
    • 13544251754 scopus 로고    scopus 로고
    • http://mathworld.wolfram.com/WallisSineFormula.html.
  • 16
    • 0012884009 scopus 로고
    • Holt, Rhinehart and Winston, New York. MR 41:5577
    • N. D. Kazarinoff, Analytic Inequalities, Holt, Rhinehart and Winston, New York, 1961. MR 41:5577
    • (1961) Analytic Inequalities
    • Kazarinoff, N.D.1
  • 19
    • 0002192812 scopus 로고
    • Inequalities for the gamma function and its logarithmic derivative
    • MR 50:10338
    • Y. L. Luke, Inequalities for the gamma function and its logarithmic derivative, Math. Balkanica (N. S.) 2 (1972), 118-123. MR 50:10338
    • (1972) Math. Balkanica (N. S.) , vol.2 , pp. 118-123
    • Luke, Y.L.1
  • 21
    • 0000976145 scopus 로고    scopus 로고
    • Some inequalities constructed by Tchebysheff's integral inequality
    • MR 2000m:26027
    • F. Qi, L.-H. Cui, and S.-L. Xu, Some inequalities constructed by Tchebysheff's integral inequality, Math. Inequal. Appl. 2 (1999), no. 4, 517-528. MR 2000m:26027
    • (1999) Math. Inequal. Appl. , vol.2 , Issue.4 , pp. 517-528
    • Qi, F.1    Cui, L.-H.2    Xu, S.-L.3
  • 22
    • 84966231869 scopus 로고
    • Analytic continuation of Riemann's zeta function and values at negative integers via Euler's transformation of series
    • MR 94d:11066
    • J. Sondow, Analytic continuation of Riemann's zeta function and values at negative integers via Euler's transformation of series, Proc. Amer. Math. Soc. 120 (1994), 421-424. MR 94d:11066
    • (1994) Proc. Amer. Math. Soc. , vol.120 , pp. 421-424
    • Sondow, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.