On gamma function inequalities
Authors:
Joaquin Bustoz and Mourad E. H. Ismail
Journal:
Math. Comp. 47 (1986), 659667
MSC:
Primary 33A15; Secondary 26D20
MathSciNet review:
856710
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We show that certain functions involving quotients of gamma functions are completely monotonic. This leads to inequalities involving gamma functions. We also establish the infinite divisibility of several probability distributions whose Laplace transforms involve quotients of gamma functions.
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 J. Dutka, "On some gamma function inequalities," SIAM J. Math. Anal., v. 16, 1985, pp. 180185. MR 772877 (86e:33002)
 [2]
 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGrawHill, New York, 1953.
 [3]
 W. Feller, An Introduction to Probability Theory and its Applications, Wiley, New York, 1966. MR 0210154 (35:1048)
 [4]
 W. Gautschi, "Some elementary inequalities relating to the gamma and incomplete gamma function," J. Math. Phys., v. 38, 1959, pp. 7781. MR 0103289 (21:2067)
 [5]
 M. E. H. Ismail, L. Lorch & M. Muldoon, "Completely monotonic functions associated with the gamma function and its qanalogues," J. Math. Anal. Appl., v. 116, 1986, pp. 19. MR 837337 (88b:33002)
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 D. K. Kazarinoff, "On Wallis' formula," Edinburgh. Math. Soc. Notes, No. 40, 1956, pp. 1921. MR 0082501 (18:560g)
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 A. Kemp, "On gamma function inequalities," Skand. Aktuarietidskr., v. 56, 1973, pp. 6569. MR 0345271 (49:10007)
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 D. Kershaw, "Some extensions of W. Gautschi's inequalities for the gamma function," Math. Comp., v. 41, 1983, pp 607611. MR 717706 (84m:33003)
 [9]
 G. N. Watson, "A note on gamma functions," Proc. Edinburgh Math. Soc. (2), v. 11, 1958/1959, Edinburgh Math. Soc. Notes, No. 42, 1959, pp. 79. MR 0117358 (22:8138)
 [10]
 D. V. Widder, The Laplace Transform, Princeton Univ. Press, Princeton, N.J., 1944.
 [11]
 J. Wimp, Sequence Transformations and Their Applications, Academic Press, New York, 1981. MR 615250 (84e:65005)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608567106
PII:
S 00255718(1986)08567106
Keywords:
Gamma function,
psi function,
complete monotonicity,
inequalities,
infinite divisibility,
Laplace transform
Article copyright:
© Copyright 1986 American Mathematical Society
