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A monotoneity property of the gamma function
Author(s):
G.
D.
Anderson;
S.-L.
Qiu
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3355-3362.
MSC (1991):
Primary 33B15;
Secondary 26A48, 26D07
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Abstract:
In this paper we obtain a monotoneity property for the gamma function that yields sharp asymptotic estimates for  as  tends to  , thus proving a conjecture about  .
References:
- [AS]
- M. Abramowitz and I. A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1965. MR 31:1400
- [Ah]
- L. V. Ahlfors, Complex Analysis, An introduction to the theory of analytic functions of one complex variable, 3rd ed., McGraw-Hill, New York, 1979. MR 80c:30001
- [A1]
- H. Alzer, Some gamma function inequalities, Math. Comp. 60 (1993), 337-346. MR 93f:33001
- [A2]
- H. Alzer, On some inequalities for the gamma and psi functions, Math. Comp. 66 (1997), 373-389. MR 97e:33004
- [ABRVV]
- 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), 1713-1723. MR 95m:33002
- [AVV]
- G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen, Special functions of quasiconformal theory, Exposition. Math. 7 (1989), 97-136. MR 90k:30032
- [BH]
- J. Böhm and E. Hertel, Polyedergeometrie
 -dimensionalen Räumen Konstanter Krümmung, Birkhäuser, Basel - Boston - Stuttgart, 1981. MR 82k:52001a - [S]
- J. Sandor, Sur la fonction gamma, Publ. Centre Rech. Math. Pures (I) (Neuchâtel) 21 (1989), 4-7.
- [SV]
- D. J. Smith and M. K. Vamanamurthy, How small is a unit ball?, Math. Mag. 62 (1989), 101-107. MR 90e:51029
- [W]
- H. F. Weinberger, Partial Differential Equations, John Wiley & Sons, New York, 1965.
- [WW]
- E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge Univ. Press, Cambridge, 1958. MR 31:2375
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Additional Information:
G.
D.
Anderson
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
anderson@math.msu.edu
S.-L.
Qiu
Affiliation:
School of Science and Arts, Hangzhou Institute of Electronics Engineering (HIEE), Hangzhou 310037, People's Republic of China
DOI:
10.1090/S0002-9939-97-04152-X
PII:
S 0002-9939(97)04152-X
Keywords:
Gamma function,
psi function,
monotoneity,
inequalities
Received by editor(s):
June 20, 1996
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1997,
American Mathematical Society
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