Further inequalities for the gamma function

Author:
Andrea Laforgia

Journal:
Math. Comp. **42** (1984), 597-600

MSC:
Primary 33A15

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736455-1

MathSciNet review:
736455

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Abstract: For and we present a method which permits us to obtain inequalities of the type , with the usual notation for the gamma function, where and are independent of *k*. Some examples are also given which improve well-known inequalities. Finally, we are also able to show in some cases that the values and in the inequalities that we obtain cannot be improved.

**[1]**M. Abramowitz & I. A. Stegun, Editors,*Handbook of Mathematical Functions*, Appl. Math. Series No. 55, National Bureau of Standards, Washington, D.C., 1964.**[2]**W. Gautschi, "Some elementary inequalities relating to the gamma and incomplete gamma function,"*J. Math. Phys.*, v. 38, 1959, pp. 77-81. MR**0103289 (21:2067)****[3]**D. Kershaw, "Some extensions of Gautschi's inequalities for the gamma function,"*Math. Comp.*, v. 41, 1983, pp. 607-611. MR**717706 (84m:33003)****[4]**L. Lorch, "Inequalities for ultraspherical polynomials and the gamma function,"*J. Approx. Theory.*(To appear.) MR**732692 (85d:33024)****[5]**G. N. Watson, "A note on gamma functions,"*Proc. Edinburgh Math. Soc.*(2), v. 11, 1958/59, Edinburgh Math. Notes No. 41, 1959, pp. 7-9. MR**0117358 (22:8138)**

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0736455-1

Article copyright:
© Copyright 1984
American Mathematical Society