-
1
-
-
0004245694
-
Handbook of mathematical functions with formulas, graphs, and mathematical tables
-
M. Abramowitz and I. A. Stegun (Eds), Series, 55 Superintendent of Documents, U.S. Government Printing Office, Washington, D.C
-
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 Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 1965.
-
(1965)
National Bureau of Standards Applied Mathematics
-
-
-
2
-
-
0042376839
-
On some inequalities for the gamma and psi functions
-
H. Alzer, On some inequalities for the gamma and psi functions, Math. Comp. 66 (1997), no. 217, 373-389.
-
(1997)
Math. Comp
, vol.66
, Issue.217
, pp. 373-389
-
-
Alzer, H.1
-
3
-
-
0000128713
-
Inequalities for zero-balanced hypergeometric functions
-
G. D. Anderson, R. W. Barnard, K. C. Richards, M. K. Vamanamurthy, and M. Vuorinen, Inequalities for zero-balanced hypergeometric functions, Trans. Amer. Math. Soc. 347 (1995), no. 5, 1713-1723.
-
(1995)
Trans. Amer. Math. Soc
, vol.347
, Issue.5
, pp. 1713-1723
-
-
Anderson, G.D.1
Barnard, R.W.2
Richards, K.C.3
Vamanamurthy, M.K.4
Vuorinen, M.5
-
4
-
-
33646870267
-
Some properties of a class of logarithmically completely monotonic functions
-
R. D. Atanassov and U. V. Tsoukrovski, Some properties of a class of logarithmically completely monotonic functions, C. R. Acad. Bulgare Sci. 41 (1988), no. 2, 21-23.
-
(1988)
C. R. Acad. Bulgare Sci
, vol.41
, Issue.2
, pp. 21-23
-
-
Atanassov, R.D.1
Tsoukrovski, U.V.2
-
5
-
-
33646380663
-
Integral representation of some functions related to the gamma function
-
C. Berg, Integral representation of some functions related to the gamma function, Mediterr. J. Math. 1 (2004), no. 4, 433-439.
-
(2004)
Mediterr. J. Math
, vol.1
, Issue.4
, pp. 433-439
-
-
Berg, C.1
-
6
-
-
33646338597
-
Logarithmically completely monotonic functions relating to the gamma function
-
Ch.-P. Chen and F. Qi, Logarithmically completely monotonic functions relating to the gamma function, J. Math. Anal. Appl. 321 (2006), no. 1, 405-411.
-
(2006)
J. Math. Anal. Appl
, vol.321
, Issue.1
, pp. 405-411
-
-
Chen, C.-P.1
Qi, F.2
-
7
-
-
21844488155
-
A stochastic approach to the gamma function
-
L. Gordon, A stochastic approach to the gamma function, Amer. Math. Monthly 101 (1994), no. 9, 858-865.
-
(1994)
Amer. Math. Monthly
, vol.101
, Issue.9
, pp. 858-865
-
-
Gordon, L.1
-
8
-
-
33645771401
-
Completely monotonic functions involving the gamma and q-gamma functions
-
A. Z. Grinshpan and M. E. H. Ismail, Completely monotonic functions involving the gamma and q-gamma functions, Proc. Amer. Math. Soc. 134 (2006), no. 4, 1153-1160.
-
(2006)
Proc. Amer. Math. Soc
, vol.134
, Issue.4
, pp. 1153-1160
-
-
Grinshpan, A.Z.1
Ismail, M.E.H.2
-
9
-
-
58549100297
-
Monotonicity and logarithmic convexity of three functions involving exponential function
-
B.-N. Guo, A.-Q. Liu, and F. Qi, Monotonicity and logarithmic convexity of three functions involving exponential function, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 15 (2008), no. 4, 387-392.
-
(2008)
J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math
, vol.15
, Issue.4
, pp. 387-392
-
-
Guo, B.-N.1
Liu, A.-Q.2
Qi, F.3
-
10
-
-
77749270240
-
Some logarithmically completely monotonic functions related to the gamma function
-
to appear
-
B.-N. Guo and F. Qi, Some logarithmically completely monotonic functions related to the gamma function, J. Korean Math. Soc. 47 (2010), to appear.
-
(2010)
J. Korean Math. Soc
, vol.47
-
-
Guo, B.-N.1
Qi, F.2
-
11
-
-
43449112661
-
Refinements and sharpenings of some double inequalities for bounding the gamma function
-
Art. 17, 5 pages; Available online at
-
B.-N. Guo, Y.-J. Zhang, and F. Qi, Refinements and sharpenings of some double inequalities for bounding the gamma function, J. Inequal. Pure Appl. Math. 9 (2008), no. 1, Art. 17, 5 pages; Available online at http://jipam.vu.edu.au/article.php?sid=953.
-
(2008)
J. Inequal. Pure Appl. Math
, vol.9
, Issue.1
-
-
Guo, B.-N.1
Zhang, Y.-J.2
Qi, F.3
-
12
-
-
45949104101
-
Monotonicity and logarithmic concavity of two functions involving exponential function
-
A.-Q. Liu, G.-F. Li, B.-N. Guo, and F. Qi, Monotonicity and logarithmic concavity of two functions involving exponential function, Internat. J. Math. Ed. Sci. Tech. 39 (2008), no. 5, 686-691.
-
(2008)
Internat. J. Math. Ed. Sci. Tech
, vol.39
, Issue.5
, pp. 686-691
-
-
Liu, A.-Q.1
Li, G.-F.2
Guo, B.-N.3
Qi, F.4
-
14
-
-
70350457627
-
Bounds for the ratio of two gamma functions
-
Art. 1; Available online at
-
F. Qi, Bounds for the ratio of two gamma functions, RGMIA Res. Rep. Coll. 11 (2008), no. 3, Art. 1; Available online at http://www.staff.vu.edu.au/rgmia/v11n3.asp.
-
(2008)
Rgmia Res. Rep. Coll
, vol.11
, Issue.3
-
-
Qi, F.1
-
15
-
-
34547224723
-
Three classes of logarithmically completely monotonic functions involving gamma and psi functions
-
F. Qi, Three classes of logarithmically completely monotonic functions involving gamma and psi functions, Integral Transforms Spec. Funct. 18 (2007), no. 7, 503-509.
-
(2007)
Integral Transforms Spec. Funct
, vol.18
, Issue.7
, pp. 503-509
-
-
Qi, F.1
-
16
-
-
3442891734
-
A complete monotonicity property of the gamma function
-
F. Qi and Ch.-P. Chen, A complete monotonicity property of the gamma function, J. Math. Anal. Appl. 296 (2004), no. 2, 603-607.
-
(2004)
J. Math. Anal. Appl
, vol.296
, Issue.2
, pp. 603-607
-
-
Qi, F.1
Chen, C.-P.2
-
17
-
-
23844476075
-
Some completely monotonic functions involving polygamma functions and an application
-
F. Qi, R.-Q. Cui, Ch.-P. Chen, and B.-N. Guo, Some completely monotonic functions involving polygamma functions and an application, J. Math. Anal. Appl. 310 (2005), no. 1, 303-308.
-
(2005)
J. Math. Anal. Appl
, vol.310
, Issue.1
, pp. 303-308
-
-
Qi, F.1
Cui, R.-Q.2
Chen, C.-P.3
Guo, B.-N.4
-
18
-
-
23844500554
-
Complete monotonicities of functions involving the gamma and digamma functions
-
Art. 8
-
F. Qi and B.-N. Guo, Complete monotonicities of functions involving the gamma and digamma functions, RGMIA Res. Rep. Coll. 7 (2004), no. 1, Art. 8, 63-72.
-
(2004)
Rgmia Res. Rep. Coll
, vol.7
, pp. 63-72
-
-
Qi, F.1
Guo, B.-N.2
-
19
-
-
33645814909
-
Some completely monotonic functions involving the gamma and polygamma functions
-
F. Qi, B.-N. Guo, and Ch.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Aust. Math. Soc. 80 (2006), no. 1, 81-88.
-
(2006)
J. Aust. Math. Soc
, vol.80
, Issue.1
, pp. 81-88
-
-
Qi, F.1
Guo, B.-N.2
Chen, C.-P.3
-
20
-
-
0004201980
-
-
Princeton University Press, Princeton
-
D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941.
-
(1941)
The Laplace Transform
-
-
Widder, D.V.1
-
21
-
-
68949156248
-
A concise proof for properties of three functions involving the exponential function
-
Sh.-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), 177-183.
-
(2009)
Appl. Math. E-notes
, vol.9
, pp. 177-183
-
-
Zhang, S.-Q.1
Guo, B.-N.2
Qi, F.3
|