-
1
-
-
0003773035
-
-
Kluwer Academic Publishers, Dordrecht, Boston, London
-
Mitrinović D.S., Pečarić J.E., and Fink A.M. Classical and New Inequalities in Analysis (1993), Kluwer Academic Publishers, Dordrecht, Boston, London
-
(1993)
Classical and New Inequalities in Analysis
-
-
Mitrinović, D.S.1
Pečarić, J.E.2
Fink, A.M.3
-
2
-
-
0004201980
-
-
Princeton University Press, Princeton
-
Widder D.V. The Laplace Transform (1941), Princeton University Press, Princeton
-
(1941)
The Laplace Transform
-
-
Widder, D.V.1
-
3
-
-
34250967495
-
Summationsmethoden und Momentfolgen I
-
Hausdorff F. Summationsmethoden und Momentfolgen I. Math. Z. 9 (1921) 74-109
-
(1921)
Math. Z.
, vol.9
, pp. 74-109
-
-
Hausdorff, F.1
-
4
-
-
0003647259
-
-
Springer, Berlin, Heidelberg, New York
-
Berg C., Christensen J.P.R., and Ressel P. Harmonic Analysis on Semigroups: Theory of Positive Deinite and Related Functions. Graduate Texts in Mathematics vol. 100 (1984), Springer, Berlin, Heidelberg, New York
-
(1984)
Graduate Texts in Mathematics
, vol.100
-
-
Berg, C.1
Christensen, J.P.R.2
Ressel, P.3
-
5
-
-
0004149470
-
Completely monotonic and related functions
-
Report 93-108, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands
-
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
-
(1993)
-
-
van Haeringen, H.1
-
6
-
-
38149147370
-
Completely monotonic rational functions and Hall's marriage theorem
-
Ball K. Completely monotonic rational functions and Hall's marriage theorem. J. Combin. Theory Ser. B 61 (1994) 118-124
-
(1994)
J. Combin. Theory Ser. B
, vol.61
, pp. 118-124
-
-
Ball, K.1
-
7
-
-
0001160530
-
Error bounds for asymptotic expansions of the ratio of two gamma functions
-
Frenzen C.L. Error bounds for asymptotic expansions of the ratio of two gamma functions. SIAM J. Math. Anal. 18 (1987) 890-896
-
(1987)
SIAM J. Math. Anal.
, vol.18
, pp. 890-896
-
-
Frenzen, C.L.1
-
9
-
-
0014926481
-
On monotonicity of the relaxation functions of viscoelastic material
-
Day W.A. On monotonicity of the relaxation functions of viscoelastic material. Proc. Cambridge Philos. Soc. 67 (1970) 503-508
-
(1970)
Proc. Cambridge Philos. Soc.
, vol.67
, pp. 503-508
-
-
Day, W.A.1
-
11
-
-
0003352027
-
Potential Theory on Locally Compact Abelian Groups
-
Springer, Berlin
-
Berg C., and Forst G. Potential Theory on Locally Compact Abelian Groups. Ergebnisse der Math. vol. 87 (1975), Springer, Berlin
-
(1975)
Ergebnisse der Math.
, vol.87
-
-
Berg, C.1
Forst, G.2
-
12
-
-
0003536178
-
-
Springer, New York
-
Bondesson L. Generalized Gamma Convolutions and Related Classes of Distributions and Densities. Lecture Notes in Statistics vol. 76 (1992), Springer, New York
-
(1992)
Lecture Notes in Statistics
, vol.76
-
-
Bondesson, L.1
-
13
-
-
0001502378
-
A probabilistic interpretation of complete monotonicity
-
Kimberling C.H. A probabilistic interpretation of complete monotonicity. Aequationes Math. 10 (1974) 152-164
-
(1974)
Aequationes Math.
, vol.10
, pp. 152-164
-
-
Kimberling, C.H.1
-
14
-
-
0004245694
-
-
Abramowitz M., and Stegun I.A. (Eds), A Wiley-Interscience Publication. Selected Government Publications. John Wiley & Sons, Inc., New York National Bureau of Standards, Washington, DC
-
In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Reprint of the 1972 edition (1984), A Wiley-Interscience Publication. Selected Government Publications. John Wiley & Sons, Inc., New York National Bureau of Standards, Washington, DC
-
(1984)
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Reprint of the 1972 edition
-
-
-
15
-
-
0004108644
-
-
Translated from the Chinese by D.-R. Guo and X.-J. Xia, World Scientific Publishing, Singapore
-
Wang Zh.-X., and Guo D.-R. Special Functions. Translated from the Chinese by D.-R. Guo and X.-J. Xia (1989), World Scientific Publishing, Singapore
-
(1989)
Special Functions
-
-
Wang, Zh.-X.1
Guo, D.-R.2
-
17
-
-
0001458111
-
Mean-value inequalities for the polygamma functions
-
Alzer H. Mean-value inequalities for the polygamma functions. Aequationes Math. 61 1 (2001) 151-161
-
(2001)
Aequationes Math.
, vol.61
, Issue.1
, pp. 151-161
-
-
Alzer, H.1
-
18
-
-
1042279113
-
Sharp inequalities for the digamma and polygamma functions
-
Alzer H. Sharp inequalities for the digamma and polygamma functions. Forum Math. 16 (2004) 181-221
-
(2004)
Forum Math.
, vol.16
, pp. 181-221
-
-
Alzer, H.1
-
19
-
-
73249141961
-
Two logarithmically completely monotonic functions connected with gamma function
-
Art. 13. Available online at http://www.staff.vu.edu.au/rgmia/v8n3.asp
-
Qi F., and Li W. Two logarithmically completely monotonic functions connected with gamma function. RGMIA Res. Rep. Coll. 8 3 (2005) 493-497. http://www.staff.vu.edu.au/rgmia/v8n3.asp Art. 13. Available online at http://www.staff.vu.edu.au/rgmia/v8n3.asp
-
(2005)
RGMIA Res. Rep. Coll.
, vol.8
, Issue.3
, pp. 493-497
-
-
Qi, F.1
Li, W.2
-
20
-
-
73249150789
-
A subadditive property of the digamma function
-
Art. 9. Available online at http://www.staff.vu.edu.au/rgmia/v8n3.asp
-
Gao P. A subadditive property of the digamma function. RGMIA Res. Rep. Coll. 8 3 (2005). http://www.staff.vu.edu.au/rgmia/v8n3.asp Art. 9. Available online at http://www.staff.vu.edu.au/rgmia/v8n3.asp
-
(2005)
RGMIA Res. Rep. Coll.
, vol.8
, Issue.3
-
-
Gao, P.1
-
21
-
-
73249117213
-
A class of completely monotonic functions involving the polygamma functions
-
Guo B.-N., Chen R.-J., and Qi F. A class of completely monotonic functions involving the polygamma functions. J. Math. Anal. Approx. Theory 1 2 (2006) 124-134
-
(2006)
J. Math. Anal. Approx. Theory
, vol.1
, Issue.2
, pp. 124-134
-
-
Guo, B.-N.1
Chen, R.-J.2
Qi, F.3
-
22
-
-
33745628039
-
Two logarithmically completely monotonic functions connected with gamma function
-
Qi F., Yang Q., and Li W. Two logarithmically completely monotonic functions connected with gamma function. Integral Transforms Spec. Funct. 17 7 (2006) 539-542
-
(2006)
Integral Transforms Spec. Funct.
, vol.17
, Issue.7
, pp. 539-542
-
-
Qi, F.1
Yang, Q.2
Li, W.3
-
23
-
-
35649001010
-
A function involving gamma function and having logarithmically absolute convexity
-
Qi F., Guo B.-N., Guo S., and Chen Sh.-X. A function involving gamma function and having logarithmically absolute convexity. Integral Transforms Spec. Funct. 18 11 (2007) 837-843
-
(2007)
Integral Transforms Spec. Funct.
, vol.18
, Issue.11
, pp. 837-843
-
-
Qi, F.1
Guo, B.-N.2
Guo, S.3
Chen, Sh.-X.4
-
24
-
-
47849114054
-
A class of k-log-convex functions and their applications to some special functions
-
Art. 21. Available online at http://www.staff.vu.edu.au/rgmia/v10n1.asp
-
Qi F., Guo S., and Guo B.-N. A class of k-log-convex functions and their applications to some special functions. RGMIA Res. Rep. Coll. 10 1 (2007). http://www.staff.vu.edu.au/rgmia/v10n1.asp Art. 21. Available online at http://www.staff.vu.edu.au/rgmia/v10n1.asp
-
(2007)
RGMIA Res. Rep. Coll.
, vol.10
, Issue.1
-
-
Qi, F.1
Guo, S.2
Guo, B.-N.3
-
25
-
-
40749136341
-
A class of k-log-convex functions and their applications to some special functions
-
Qi F., Guo S., Guo B.-N., and Chen Sh.-X. A class of k-log-convex functions and their applications to some special functions. Integral Transforms Spec. Funct. 19 3 (2008) 195-200
-
(2008)
Integral Transforms Spec. Funct.
, vol.19
, Issue.3
, pp. 195-200
-
-
Qi, F.1
Guo, S.2
Guo, B.-N.3
Chen, Sh.-X.4
-
26
-
-
47849114054
-
Note on a class of completely monotonic functions involving the polygamma functions
-
Art. 5. Available online at http://www.staff.vu.edu.au/rgmia/v10n1.asp
-
Qi F., Guo S., and Guo B.-N. Note on a class of completely monotonic functions involving the polygamma functions. RGMIA Res. Rep. Coll. 10 1 (2007). http://www.staff.vu.edu.au/rgmia/v10n1.asp Art. 5. Available online at http://www.staff.vu.edu.au/rgmia/v10n1.asp
-
(2007)
RGMIA Res. Rep. Coll.
, vol.10
, Issue.1
-
-
Qi, F.1
Guo, S.2
Guo, B.-N.3
-
27
-
-
47849122739
-
A new upper bound in the second Kershaw's double inequality and its generalizations
-
Available online at http://dx.doi.org/10.1016/j.cam.2007.07.037
-
Qi F., Guo S., and Chen Sh.-X. A new upper bound in the second Kershaw's double inequality and its generalizations. J. Comput. Appl. Math. 220 1-2 (2008) 111-118. http://dx.doi.org/10.1016/j.cam.2007.07.037 Available online at http://dx.doi.org/10.1016/j.cam.2007.07.037
-
(2008)
J. Comput. Appl. Math.
, vol.220
, Issue.1-2
, pp. 111-118
-
-
Qi, F.1
Guo, S.2
Chen, Sh.-X.3
-
28
-
-
48549090221
-
Refinements, extensions and generalizations of the second Kershaw's double inequality
-
Qi F., Li X.-A., and Chen Sh.-X. Refinements, extensions and generalizations of the second Kershaw's double inequality. Math. Inequal. Appl. 11 3 (2008) 457-465
-
(2008)
Math. Inequal. Appl.
, vol.11
, Issue.3
, pp. 457-465
-
-
Qi, F.1
Li, X.-A.2
Chen, Sh.-X.3
-
29
-
-
33645019224
-
Sub- and super-additive properties of Fejér's sine polynomial
-
Alzer H., and Koumandos S. Sub- and super-additive properties of Fejér's sine polynomial. Bull. London Math. Soc. 38 2 (2006) 261-268
-
(2006)
Bull. London Math. Soc.
, vol.38
, Issue.2
, pp. 261-268
-
-
Alzer, H.1
Koumandos, S.2
-
30
-
-
0141503441
-
A subadditive property of the gamma function
-
Alzer H., and Ruscheweyh S. A subadditive property of the gamma function. J. Math. Anal. Appl. 285 (2003) 564-577
-
(2003)
J. Math. Anal. Appl.
, vol.285
, pp. 564-577
-
-
Alzer, H.1
Ruscheweyh, S.2
-
31
-
-
0032654421
-
A submultiplicative property of the psi function
-
Alzer H., and Ruehr O.G. A submultiplicative property of the psi function. J. Comput. Appl. Math. 101 (1999) 53-60
-
(1999)
J. Comput. Appl. Math.
, vol.101
, pp. 53-60
-
-
Alzer, H.1
Ruehr, O.G.2
-
32
-
-
41849114947
-
Convexities of some functions involving the polygamma functions
-
Cao J., Niu D.-W., and Qi F. Convexities of some functions involving the polygamma functions. Appl. Math. E-Notes 8 (2008) 53-57
-
(2008)
Appl. Math. E-Notes
, vol.8
, pp. 53-57
-
-
Cao, J.1
Niu, D.-W.2
Qi, F.3
-
33
-
-
73249124628
-
-
F. Qi, B.-N. Guo, A note on additivity of polygamma functions. Available online at http://arxiv.org/abs/0903.0888
-
F. Qi, B.-N. Guo, A note on additivity of polygamma functions. Available online at http://arxiv.org/abs/0903.0888
-
-
-
-
34
-
-
47849114054
-
Subadditive and superadditive properties of polygamma functions
-
Art. 4. Available online at http://www.staff.vu.edu.au/rgmia/v10(E).asp
-
Qi F., and Guo B.-N. Subadditive and superadditive properties of polygamma functions. RGMIA Res. Rep. Coll. 10 Suppl. (2007). http://www.staff.vu.edu.au/rgmia/v10(E).asp Art. 4. Available online at http://www.staff.vu.edu.au/rgmia/v10(E).asp
-
(2007)
RGMIA Res. Rep. Coll.
, vol.10
, Issue.SUPPL
-
-
Qi, F.1
Guo, B.-N.2
-
35
-
-
73249136531
-
A double inequality for the gamma and psi functions
-
Zhang X.-M., and Chu Y.-M. A double inequality for the gamma and psi functions. Int. J. Mod. Math. 3 1 (2008) 67-73
-
(2008)
Int. J. Mod. Math.
, vol.3
, Issue.1
, pp. 67-73
-
-
Zhang, X.-M.1
Chu, Y.-M.2
-
36
-
-
34047117831
-
Geometric convexity of a function involving gamma function and applications to inequality theory
-
Art. 17. Available online at http://jipam.vu.edu.au/article.php?sid=830
-
Zhang X.-M., Xu T.-Q., and Situ L.-B. Geometric convexity of a function involving gamma function and applications to inequality theory. J. Inequal. Pure Appl. Math. 8 1 (2007). http://jipam.vu.edu.au/article.php%3Fsid%3D830 Art. 17. Available online at http://jipam.vu.edu.au/article.php?sid=830
-
(2007)
J. Inequal. Pure Appl. Math.
, vol.8
, Issue.1
-
-
Zhang, X.-M.1
Xu, T.-Q.2
Situ, L.-B.3
-
37
-
-
33646870267
-
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
-
38
-
-
33645766365
-
Complete monotonicities of functions involving the gamma and digamma functions
-
Art. 8. Available online at http://www.staff.vu.edu.au/rgmia/v7n1.asp
-
Qi F., and Guo B.-N. Complete monotonicities of functions involving the gamma and digamma functions. RGMIA Res. Rep. Coll. 7 1 (2004) 63-72. http://www.staff.vu.edu.au/rgmia/v7n1.asp Art. 8. Available online 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
-
39
-
-
77749270240
-
-
F. Qi, B.-N. Guo, Some logarithmically completely monotonic functions related to the gamma function, J. Korean Math. Soc. 47 (1) (2010) (in press)
-
F. Qi, B.-N. Guo, Some logarithmically completely monotonic functions related to the gamma function, J. Korean Math. Soc. 47 (1) (2010) (in press)
-
-
-
-
40
-
-
33645778397
-
Some completely monotonic functions involving the gamma and polygamma functions
-
Art. 5. Available online at http://www.staff.vu.edu.au/rgmia/v7n1.asp
-
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) 31-36. http://www.staff.vu.edu.au/rgmia/v7n1.asp Art. 5. Available online at http://www.staff.vu.edu.au/rgmia/v7n1.asp
-
(2004)
RGMIA Res. Rep. Coll.
, vol.7
, Issue.1
, pp. 31-36
-
-
Qi, F.1
Guo, B.-N.2
Chen, Ch.-P.3
-
41
-
-
33645814909
-
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. Aust. Math. Soc. 80 (2006) 81-88
-
(2006)
J. Aust. Math. Soc.
, vol.80
, pp. 81-88
-
-
Qi, F.1
Guo, B.-N.2
Chen, Ch.-P.3
-
42
-
-
3442891734
-
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 (2004) 603-607
-
(2004)
J. Math. Anal. Appl.
, vol.296
, pp. 603-607
-
-
Qi, F.1
Chen, Ch.-P.2
-
43
-
-
33646380663
-
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
-
45
-
-
33645771401
-
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
-
46
-
-
37249046597
-
Generalizations of a theorem of I. Schur
-
Art. 15. Available online at http://www.staff.vu.edu.au/rgmia/v9n3.asp
-
Qi F., Li W., and Guo B.-N. Generalizations of a theorem of I. Schur. RGMIA Res. Rep. Coll. 9 3 (2006). http://www.staff.vu.edu.au/rgmia/v9n3.asp Art. 15. Available online at http://www.staff.vu.edu.au/rgmia/v9n3.asp
-
(2006)
RGMIA Res. Rep. Coll.
, vol.9
, Issue.3
-
-
Qi, F.1
Li, W.2
Guo, B.-N.3
-
47
-
-
33645140646
-
On infinitely divisible matrices, kernels and functions
-
Horn R.A. On infinitely divisible matrices, kernels and functions. Z. Wahrscheinlichkeitstheor. Verwandte. Geb 8 (1967) 219-230
-
(1967)
Z. Wahrscheinlichkeitstheor. Verwandte. Geb
, vol.8
, pp. 219-230
-
-
Horn, R.A.1
-
48
-
-
0000270382
-
Inequalities and monotonicity properties for gamma and q-gamma functions
-
Zahar R.V.M. (Ed), BirkhRauser, Basel
-
Ismail M.E.H., and Muldoon M.E. Inequalities and monotonicity properties for gamma and q-gamma functions. In: Zahar R.V.M. (Ed). Approximation and Computation: A Festschrift in Honour of Walter Gautschi, ISNM vol. 119 (1994), BirkhRauser, Basel 309-323
-
(1994)
Approximation and Computation: A Festschrift in Honour of Walter Gautschi, ISNM
, vol.119
, pp. 309-323
-
-
Ismail, M.E.H.1
Muldoon, M.E.2
-
49
-
-
0002146064
-
Some monotonicity properties and characterizations of the gamma function
-
Muldoon M.E. Some monotonicity properties and characterizations of the gamma function. Aequationes Math. 18 (1978) 54-63
-
(1978)
Aequationes Math.
, vol.18
, pp. 54-63
-
-
Muldoon, M.E.1
-
50
-
-
36348957497
-
A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums
-
Qi F. A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums. ANZIAM J. 48 4 (2007) 523-532
-
(2007)
ANZIAM J.
, vol.48
, Issue.4
, pp. 523-532
-
-
Qi, F.1
-
51
-
-
34047144395
-
A completely monotonic function involving divided differences of psi and polygamma functions and an application
-
Art. 8. Available online at http://www.staff.vu.edu.au/rgmia/v9n4.asp
-
Qi F. A completely monotonic function involving divided differences of psi and polygamma functions and an application. RGMIA Res. Rep. Coll. 9 4 (2006). http://www.staff.vu.edu.au/rgmia/v9n4.asp Art. 8. Available online at http://www.staff.vu.edu.au/rgmia/v9n4.asp
-
(2006)
RGMIA Res. Rep. Coll.
, vol.9
, Issue.4
-
-
Qi, F.1
-
52
-
-
34047144395
-
The best bounds in Kershaw's inequality and two completely monotonic functions
-
Art. 2. Available online at http://www.staff.vu.edu.au/rgmia/v9n4.asp
-
Qi F. The best bounds in Kershaw's inequality and two completely monotonic functions. RGMIA Res. Rep. Coll. 9 4 (2006). http://www.staff.vu.edu.au/rgmia/v9n4.asp Art. 2. Available online at http://www.staff.vu.edu.au/rgmia/v9n4.asp
-
(2006)
RGMIA Res. Rep. Coll.
, vol.9
, Issue.4
-
-
Qi, F.1
-
53
-
-
34547224723
-
Three classes of logarithmically completely monotonic functions involving gamma and psi functions
-
Qi F. Three classes of logarithmically completely monotonic functions involving gamma and psi functions. Integral Transforms Spec. Funct. 18 7 (2007) 503-509
-
(2007)
Integral Transforms Spec. Funct.
, vol.18
, Issue.7
, pp. 503-509
-
-
Qi, F.1
-
54
-
-
73249123569
-
Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
-
Available online at http://dx.doi.org/10.3934/cpaa.2009.8.1975
-
Qi F., and Guo B.-N. Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications. Commun. Pure Appl. Anal. 8 6 (2009) 1975-1989. http://dx.doi.org/10.3934/cpaa.2009.8.1975 Available online at http://dx.doi.org/10.3934/cpaa.2009.8.1975
-
(2009)
Commun. Pure Appl. Anal.
, vol.8
, Issue.6
, pp. 1975-1989
-
-
Qi, F.1
Guo, B.-N.2
-
55
-
-
33646338597
-
Logarithmically completely monotonic functions relating to the gamma function
-
Chen Ch.-P., and Qi F. Logarithmically completely monotonic functions relating to the gamma function. J. Math. Anal. Appl. 321 1 (2006) 405-411
-
(2006)
J. Math. Anal. Appl.
, vol.321
, Issue.1
, pp. 405-411
-
-
Chen, Ch.-P.1
Qi, F.2
|