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Volumn 21, Issue 2, 2010, Pages 153-164

Some properties of functions related to the gamma and psi functions

Author keywords

Absolutely monotonic functions; Completely monotonic functions; Gamma function; Logarithmically completely monotonic functions; Psi function; Strongly completely monotonic functions

Indexed keywords


EID: 71649091201     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652460903064216     Document Type: Article
Times cited : (47)

References (25)
  • 1
    • 71649097316 scopus 로고
    • M. Abramowitz and I.A. Stegun (eds), Applied Mathematics Series 55, Ninth Printing, National Bureau of Standards, Washington, DC
    • M. Abramowitz and I.A. Stegun (eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series 55, Ninth Printing, National Bureau of Standards, Washington, DC, 1972.
    • (1972) Handbook of Mathematical Functions with Formulas Graphs, and Mathematical Tables
  • 2
    • 34548104410 scopus 로고    scopus 로고
    • Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions
    • C.-P. Chen, Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions, J. Math. Anal. Appl. 336 (2007), pp. 812-822.
    • (2007) J. Math. Anal. Appl. , vol.336 , pp. 812-822
    • Chen, C.-P.1
  • 3
    • 71649084327 scopus 로고    scopus 로고
    • Completely monotonic functions related to the gamma functions
    • (Article 3). Available at
    • C.-P. Chen and F. Qi, Completely monotonic functions related to the gamma functions, RGMIA Res. Rep. Coll. 8(2) (2005), 195-200 (Article 3). Available at http://www.staff.vu.edu.au/rgmia/v8n2.asp.
    • (2005) Rgmia Res. Rep. Coll. , vol.8 , Issue.2 , pp. 195-200
    • Chen, C.-P.1    Qi, F.2
  • 4
    • 0011526838 scopus 로고
    • Sur un théorème de M. S. Bernstein relatif à la transformation de Laplace-Stieltjes
    • (in French)
    • J. Dubourdieu, Sur un théorème de M. S. Bernstein relatif à la transformation de Laplace-Stieltjes, Compositio Math. 7 (1939), 96-111 (in French).
    • (1939) Compositio Math. , vol.7 , pp. 96-111
    • Dubourdieu, J.1
  • 5
    • 71649085838 scopus 로고    scopus 로고
    • A class of completely monotonic functions related to the remainder of Binet's formula with applications
    • S. Guo and F. Qi, A class of completely monotonic functions related to the remainder of Binet's formula with applications, Tamsui Oxford J. Math. Sci. 25 (2009), pp. 9-14.
    • (2009) Tamsui Oxford J. Math. Sci. , vol.25 , pp. 9-14
    • Guo, S.1    Qi, F.2
  • 6
    • 0030524935 scopus 로고    scopus 로고
    • Completely monotonic and related functions
    • H. van Haeringen, Completely monotonic and related functions, J. Math. Anal. Appl. 204 (1996), pp. 389-408.
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 389-408
    • van Haeringen, H.1
  • 7
    • 60749112307 scopus 로고    scopus 로고
    • Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
    • S. Koumandos and H.L. Pedersen, Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function, J. Math. Anal. Appl. 355 (2009), pp. 33-40.
    • (2009) J. Math. Anal. Appl. , vol.355 , pp. 33-40
    • Koumandos, S.1    Pedersen, H.L.2
  • 8
    • 2342560615 scopus 로고    scopus 로고
    • Reciprocally convex functions
    • M. Merkle, Reciprocally convex functions, J. Math. Anal. Appl. 293 (2004), pp. 210-218.
    • (2004) J. Math. Anal. Appl. , vol.293 , pp. 210-218
    • Merkle, M.1
  • 10
    • 0000407393 scopus 로고    scopus 로고
    • Generalized weighted mean values with two parameters
    • F. Qi, Generalized weighted mean values with two parameters, Proc. Roy. Soc. London Ser. A Math. Phys. Engrg. Sci. 454 (1978) (1998), pp. 2723-2732.
    • (1998) Proc. Roy. Soc. London Ser. a Math. Phys. Engrg. Sci. , vol.454 , Issue.1978 , pp. 2723-2732
    • Qi, F.1
  • 11
    • 33645766365 scopus 로고    scopus 로고
    • Complete monotonicities of functions involving the gamma and digamma functions
    • (Article 8). Available at
    • F. Qi and B.-N. Guo, Complete monotonicities of functions involving the gamma and digamma functions, RGMIA Res. Rep. Coll. 7(1) (2004), pp. 63-72 (Article 8). Available at http://www.staff.vu.edu.au/rgmia/v7n1.asp.
    • (2004) Rgmia Res. Rep. Coll , vol.7 , Issue.1 , pp. 63-72
    • Qi, F.1    Guo, B.-N.2
  • 15
    • 71649086217 scopus 로고    scopus 로고
    • Monotonic properties of differences for remainders of psi function
    • (Article 16), Available at
    • F. Qi, D.-W. Niu, and B.-N. Guo, Monotonic properties of differences for remainders of psi function, RGMIA Res. Rep. Coll. 8(4) (2005), pp. 683-690 (Article 16). Available at http://www.staff.vu.edu.au/rgmia/v8n4.asp.
    • (2005) Rgmia Res. Rep. Coll. , vol.8 , Issue.4 , pp. 683-690
    • Qi, F.1    Niu, D.-W.2    Guo, B.-N.3
  • 16
    • 33645814909 scopus 로고    scopus 로고
    • Some completely monotonic functions involving the gamma and polygamma functions
    • F. Qi, B.-N. Guo, and C.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Aust. Math. Soc. 80 (2006), pp. 81-88.
    • (2006) J. Aust. Math. Soc. , vol.80 , pp. 81-88
    • Qi, F.1    Guo, B.-N.2    Chen, C.-P.3
  • 17
    • 37249046597 scopus 로고    scopus 로고
    • Generalizations of a theorem of I. Schur
    • (Article 15). Available at
    • F. Qi, W. Li, and B.-N. Guo, Generalizations of a theorem of I. Schur, RGMIA Res. Rep. Coll. 9(3) (2006), pp. 1-10 (Article 15). Available at http://www.staff.vu.edu.au/rgmia/v9n3.asp.
    • (2006) Rgmia Res. Rep. Coll. , vol.9 , Issue.3 , pp. 1-10
    • Qi, F.1    Li, W.2    Guo, B.-N.3
  • 18
    • 71649099826 scopus 로고    scopus 로고
    • Monotonic properties of differences for remainders of psi function
    • F. Qi, D.-W. Niu, and B.-N. Guo, Monotonic properties of differences for remainders of psi function, Internat. J. Pure Appl. Math. Sci. 4(1) (2007).
    • (2007) Internat. J. Pure Appl. Math. Sci. , vol.4 , Issue.1
    • Qi, F.1    Niu, D.-W.2    Guo, B.-N.3
  • 19
    • 14944340570 scopus 로고    scopus 로고
    • Some properties of the gamma and psi functions with applications
    • S.-L. Qiu and M. Vuorinen, Some properties of the gamma and psi functions with applications, Math. Comput. 74 (2004), pp. 723-742.
    • (2004) Math. Comput. , vol.74 , pp. 723-742
    • Qiu, S.-L.1    Vuorinen, M.2
  • 20
    • 71649083093 scopus 로고    scopus 로고
    • On a limit involving the Euler-gamma function
    • J. Sándor, On a limit involving the Euler-gamma function, Octogon Math. Mag. 11(1) (2004), pp. 262-264.
    • (2004) Octogon Math. Mag. , vol.11 , Issue.1 , pp. 262-264
    • Sándor, J.1
  • 21
    • 0012100570 scopus 로고
    • Superadditive functions and a statistical application
    • S.Y. Trimble, J. Wells, and F. T. Wright, Superadditive functions and a statistical application, SIAM J. Math. Anal. 20 (1989), pp. 1255-1259.
    • (1989) Siam J. Math. Anal. , vol.20 , pp. 1255-1259
    • Trimble, S.Y.1    Wells, J.2    Wright, F.T.3
  • 22
    • 0004108644 scopus 로고
    • (Translated From the Chinese By D.-r. Guo and X.-j. Xia), World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong
    • Z.-X. Wang and D.-R. Guo, Special Functions (translated from the Chinese by D.-R. Guo and X.-J. Xia), World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1989.
    • (1989) Special Functions
    • Wang, Z.-X.1    Guo, D.-R.2
  • 23
    • 71649113476 scopus 로고    scopus 로고
    • From MathWorld - A Wolfram Web Resource. Available at
    • E.W. Weisstein, Faá di Bruno's Formula, From MathWorld - A Wolfram Web Resource. Available at http://mathworld.wolfram.com/FaadiBrunosFormula.html.
    • Faá Di Bruno's Formula
    • Weisstein, E.W.1
  • 24
  • 25
    • 68949156248 scopus 로고    scopus 로고
    • A concise proof for properties of three functions involving the exponential function
    • S.-Q. Zhang, B.-N. Guo, and F. Qi, A concise proof for properties of three functions involving the exponential function, Appl. Math. E-Notes 9 (2009), pp. 177-183.
    • (2009) Appl. Math. E-notes , vol.9 , pp. 177-183
    • Zhang, S.-Q.1    Guo, B.-N.2    Qi, F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.