메뉴 건너뛰기




Volumn 206, Issue 2, 2007, Pages 1007-1014

A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality

Author keywords

Best bound; Extension; Gamma function; Generalization; J.G. Wendel's inequality; Logarithmically completely monotonic function; Open problem; Refinement; The first Kershaw's double inequality

Indexed keywords

COMPUTATIONAL MECHANICS; EULER EQUATIONS; PROBLEM SOLVING;

EID: 34047143717     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.09.005     Document Type: Article
Times cited : (38)

References (31)
  • 1
    • 34249813173 scopus 로고    scopus 로고
    • M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, vol. 55, 4th printing, with corrections, Washington, 1965.
  • 2
    • 33646870267 scopus 로고
    • Some properties of a class of logarithmically completely monotonic functions
    • Atanassov R.D., and Tsoukrovski U.V. Some properties of a class of logarithmically completely monotonic functions. C.R. Acad. Bulgare Sci. 41 2 (1988) 21-23
    • (1988) C.R. Acad. Bulgare Sci. , vol.41 , Issue.2 , pp. 21-23
    • Atanassov, R.D.1    Tsoukrovski, U.V.2
  • 3
    • 33646380663 scopus 로고    scopus 로고
    • Integral representation of some functions related to the gamma function
    • Berg C. Integral representation of some functions related to the gamma function. Mediterr. J. Math. 1 4 (2004) 433-439
    • (2004) Mediterr. J. Math. , vol.1 , Issue.4 , pp. 433-439
    • Berg, C.1
  • 4
    • 84966216618 scopus 로고
    • On gamma function inequalities
    • Bustoz J., and Ismail M.E.H. On gamma function inequalities. Math. Comp. 47 (1986) 659-667
    • (1986) Math. Comp. , vol.47 , pp. 659-667
    • Bustoz, J.1    Ismail, M.E.H.2
  • 5
    • 27844459163 scopus 로고    scopus 로고
    • Monotonicity and convexity for the gamma function
    • Art. 100, available online at 〈http://jipam.vu.edu.au/article.php?sid=574〉
    • Chen Ch.-P. Monotonicity and convexity for the gamma function. J. Inequal. Pure Appl. Math. 6 4 (2005). http://jipam.vu.edu.au/article.php?sid=574 Art. 100, available online at 〈http://jipam.vu.edu.au/article.php?sid=574〉
    • (2005) J. Inequal. Pure Appl. Math. , vol.6 , Issue.4
    • Chen, Ch.-P.1
  • 7
    • 84912062631 scopus 로고
    • The gamma function inequalities of Gurland and Gautschi
    • Erber T. The gamma function inequalities of Gurland and Gautschi. Scand. Actuar. J. 1960 (1961) 27-28
    • (1961) Scand. Actuar. J. , vol.1960 , pp. 27-28
    • Erber, T.1
  • 8
    • 85171841264 scopus 로고
    • Some elementary inequalities relating to the gamma and incomplete gamma function
    • Gautschi W. Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1959) 77-81
    • (1959) J. Math. Phys. , vol.38 , pp. 77-81
    • Gautschi, W.1
  • 9
    • 33645771401 scopus 로고    scopus 로고
    • Completely monotonic functions involving the gamma and q-gamma functions
    • Grinshpan A.Z., and Ismail M.E.H. Completely monotonic functions involving the gamma and q-gamma functions. Proc. Amer. Math. Soc. 134 (2006) 1153-1160
    • (2006) Proc. Amer. Math. Soc. , vol.134 , pp. 1153-1160
    • Grinshpan, A.Z.1    Ismail, M.E.H.2
  • 10
    • 0013201328 scopus 로고    scopus 로고
    • Inequalities for generalized weighted mean values of convex function
    • RGMIA Res. Rep. Coll. 2(7) (1999) Art. 11, 1059-1065, available online at 〈http://rgmia.vu.edu.au/v2n7.html〉
    • Guo B.-N., and Qi F. Inequalities for generalized weighted mean values of convex function. Math. Inequal. Appl. 4 2 (2001) 195-202. http://rgmia.vu.edu.au/v2n7.html RGMIA Res. Rep. Coll. 2(7) (1999) Art. 11, 1059-1065, available online at 〈http://rgmia.vu.edu.au/v2n7.html〉
    • (2001) Math. Inequal. Appl. , vol.4 , Issue.2 , pp. 195-202
    • Guo, B.-N.1    Qi, F.2
  • 11
    • 33645140646 scopus 로고
    • On infinitely divisible matrices, kernels and functions
    • Horn R.A. On infinitely divisible matrices, kernels and functions. Z. Wahrscheinlichkeitstheorie Verw. Geb. 8 (1967) 219-230
    • (1967) Z. Wahrscheinlichkeitstheorie Verw. Geb. , vol.8 , pp. 219-230
    • Horn, R.A.1
  • 13
    • 84966228652 scopus 로고
    • Some extensions of W. Gautschi's inequalities for the gamma function
    • Kershaw D. Some extensions of W. Gautschi's inequalities for the gamma function. Math. Comp. 41 (1983) 607-611
    • (1983) Math. Comp. , vol.41 , pp. 607-611
    • Kershaw, D.1
  • 14
    • 0000407393 scopus 로고    scopus 로고
    • Generalized weighted mean values with two parameters
    • Qi F. Generalized weighted mean values with two parameters. Roy. Soc. London Proc. Ser. A Math. Phys. Eng. Sci. 454 1978 (1998) 2723-2732
    • (1998) Roy. Soc. London Proc. Ser. A Math. Phys. Eng. Sci. , vol.454 , Issue.1978 , pp. 2723-2732
    • Qi, F.1
  • 15
    • 10044296224 scopus 로고    scopus 로고
    • Generalized abstracted mean values
    • Art. 4, available online at 〈http://jipam.vu.edu.au/article.php?sid=97〉. RGMIA Res. Rep. Coll. 2(5) (1999) Art. 4, 633-642, available online at 〈http://rgmia.vu.edu.au/v2n5.html〉
    • Qi F. Generalized abstracted mean values. J. Inequal. Pure Appl. Math. 1 1 (2000). http://jipam.vu.edu.au/article.php?sid=97 Art. 4, available online at 〈http://jipam.vu.edu.au/article.php?sid=97〉. RGMIA Res. Rep. Coll. 2(5) (1999) Art. 4, 633-642, available online at 〈http://rgmia.vu.edu.au/v2n5.html〉
    • (2000) J. Inequal. Pure Appl. Math. , vol.1 , Issue.1
    • Qi, F.1
  • 16
    • 0036001642 scopus 로고    scopus 로고
    • Monotonicity results and inequalities for the gamma and incomplete gamma functions
    • RGMIA Res. Rep. Coll. 2(7) (1999) Art. 7, 1027-1034, available online at 〈http://rgmia.vu.edu.au/v2n7.html〉
    • Qi F. Monotonicity results and inequalities for the gamma and incomplete gamma functions. Math. Inequal. Appl. 5 1 (2002) 61-67. http://rgmia.vu.edu.au/v2n7.html RGMIA Res. Rep. Coll. 2(7) (1999) Art. 7, 1027-1034, available online at 〈http://rgmia.vu.edu.au/v2n7.html〉
    • (2002) Math. Inequal. Appl. , vol.5 , Issue.1 , pp. 61-67
    • Qi, F.1
  • 17
    • 27844479859 scopus 로고    scopus 로고
    • The extended mean values: definition, properties, monotonicities, comparison, convexities, generalizations, and applications
    • RGMIA Res. Rep. Coll. 5(1) (2002) Art. 5, 57-80, available online at 〈http://rgmia.vu.edu.au/v5n1.html〉
    • Qi F. The extended mean values: definition, properties, monotonicities, comparison, convexities, generalizations, and applications. Cubo Mat. Educ. 5 3 (2003) 63-90. http://rgmia.vu.edu.au/v5n1.html RGMIA Res. Rep. Coll. 5(1) (2002) Art. 5, 57-80, available online at 〈http://rgmia.vu.edu.au/v5n1.html〉
    • (2003) Cubo Mat. Educ. , vol.5 , Issue.3 , pp. 63-90
    • Qi, F.1
  • 18
    • 34249780598 scopus 로고    scopus 로고
    • Certain logarithmically N-alternating monotonic functions involving gamma and q-gamma functions
    • Art. 5, available online at 〈http://rgmia.vu.edu.au/v8n3.html〉
    • Qi F. Certain logarithmically N-alternating monotonic functions involving gamma and q-gamma functions. RGMIA Res. Rep. Coll. 8 3 (2005). http://rgmia.vu.edu.au/v8n3.html Art. 5, available online at 〈http://rgmia.vu.edu.au/v8n3.html〉
    • (2005) RGMIA Res. Rep. Coll. , vol.8 , Issue.3
    • Qi, F.1
  • 19
    • 34249808898 scopus 로고    scopus 로고
    • Monotonicity and logarithmic convexity for a class of elementary functions involving the exponential function
    • Art. 3, available online at 〈http://rgmia.vu.edu.au/v9n3.html〉
    • Qi F. Monotonicity and logarithmic convexity for a class of elementary functions involving the exponential function. RGMIA Res. Rep. Coll. 9 3 (2006). http://rgmia.vu.edu.au/v9n3.html Art. 3, available online at 〈http://rgmia.vu.edu.au/v9n3.html〉
    • (2006) RGMIA Res. Rep. Coll. , vol.9 , Issue.3
    • Qi, F.1
  • 20
    • 34249823428 scopus 로고    scopus 로고
    • Three-log-convexity for a class of elementary functions involving exponential function
    • Qi F. Three-log-convexity for a class of elementary functions involving exponential function. J. Math. Anal. Approx. Theory 1 2 (2006) 100-103
    • (2006) J. Math. Anal. Approx. Theory , vol.1 , Issue.2 , pp. 100-103
    • Qi, F.1
  • 21
    • 34249784895 scopus 로고    scopus 로고
    • F. Qi, J. Cao, D.-W. Niu, Four logarithmically completely monotonic functions involving gamma function, submitted for publication.
  • 22
    • 34249800432 scopus 로고    scopus 로고
    • Four logarithmically completely monotonic functions involving gamma function and originating from problems of traffic flow
    • Art 9, available online at 〈http://rgmia.vu.edu.au/v9n3.html〉
    • Qi F., Cao J., and Niu D.-W. Four logarithmically completely monotonic functions involving gamma function and originating from problems of traffic flow. RGMIA Res. Rep. Coll. 9 3 (2006). http://rgmia.vu.edu.au/v9n3.html Art 9, available online at 〈http://rgmia.vu.edu.au/v9n3.html〉
    • (2006) RGMIA Res. Rep. Coll. , vol.9 , Issue.3
    • Qi, F.1    Cao, J.2    Niu, D.-W.3
  • 23
    • 3442891734 scopus 로고    scopus 로고
    • A complete monotonicity property of the gamma function
    • Qi F., and Chen Ch.-P. A complete monotonicity property of the gamma function. J. Math. Anal. Appl. 296 2 (2004) 603-607
    • (2004) J. Math. Anal. Appl. , vol.296 , Issue.2 , pp. 603-607
    • Qi, F.1    Chen, Ch.-P.2
  • 24
    • 33645766365 scopus 로고    scopus 로고
    • Complete monotonicities of functions involving the gamma and digamma functions
    • Art. 8, 63-72, available online at 〈http://rgmia.vu.edu.au/v7n1.html〉
    • Qi F., and Guo B.-N. Complete monotonicities of functions involving the gamma and digamma functions. RGMIA Res. Rep. Coll. 7 1 (2004). http://rgmia.vu.edu.au/v7n1.html Art. 8, 63-72, available online at 〈http://rgmia.vu.edu.au/v7n1.html〉
    • (2004) RGMIA Res. Rep. Coll. , vol.7 , Issue.1
    • Qi, F.1    Guo, B.-N.2
  • 25
    • 33645778397 scopus 로고    scopus 로고
    • Some completely monotonic functions involving the gamma and polygamma functions
    • Art. 5, 31-36, available online at 〈http://rgmia.vu.edu.au/v7n1.html〉
    • Qi F., Guo B.-N., and Chen Ch.-P. Some completely monotonic functions involving the gamma and polygamma functions. RGMIA Res. Rep. Coll. 7 1 (2004). http://rgmia.vu.edu.au/v7n1.html Art. 5, 31-36, available online at 〈http://rgmia.vu.edu.au/v7n1.html〉
    • (2004) RGMIA Res. Rep. Coll. , vol.7 , Issue.1
    • Qi, F.1    Guo, B.-N.2    Chen, Ch.-P.3
  • 26
    • 33645814909 scopus 로고    scopus 로고
    • Some completely monotonic functions involving the gamma and polygamma functions
    • Qi F., Guo B.-N., and Chen Ch.-P. Some completely monotonic functions involving the gamma and polygamma functions. J. Austral. Math. Soc. 80 (2006) 81-88
    • (2006) J. Austral. Math. Soc. , vol.80 , pp. 81-88
    • Qi, F.1    Guo, B.-N.2    Chen, Ch.-P.3
  • 27
    • 33747056370 scopus 로고    scopus 로고
    • The best bounds in Gautschi-Kershaw inequalities
    • RGMIA Res. Rep. Coll. 8(2) (2005) Art. 17, available online at 〈http://rgmia.vu.edu.au/v8n2.html〉
    • Qi F., Guo B.-N., and Chen Ch.-P. The best bounds in Gautschi-Kershaw inequalities. Math. Inequal. Appl. 9 3 (2006) 427-436. http://rgmia.vu.edu.au/v8n2.html RGMIA Res. Rep. Coll. 8(2) (2005) Art. 17, available online at 〈http://rgmia.vu.edu.au/v8n2.html〉
    • (2006) Math. Inequal. Appl. , vol.9 , Issue.3 , pp. 427-436
    • Qi, F.1    Guo, B.-N.2    Chen, Ch.-P.3
  • 29
    • 34249821123 scopus 로고    scopus 로고
    • H. van Haeringen, Completely monotonic and related functions, Report 93-108, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands, 1993.
  • 30
    • 0041882790 scopus 로고
    • Note on the gamma function
    • Wendel J. Note on the gamma function. Amer. Math. Monthly 55 (1948) 563-564
    • (1948) Amer. Math. Monthly , vol.55 , pp. 563-564
    • Wendel, J.1
  • 31


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.