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]**Walter Gautschi,*Some elementary inequalities relating to the gamma and incomplete gamma function*, J. Math. and Phys.**38**(1959/60), 77–81. MR**0103289**, https://doi.org/10.1002/sapm195938177**[3]**D. Kershaw,*Some extensions of W. Gautschi’s inequalities for the gamma function*, Math. Comp.**41**(1983), no. 164, 607–611. MR**717706**, https://doi.org/10.1090/S0025-5718-1983-0717706-5**[4]**Lee Lorch,*Inequalities for ultraspherical polynomials and the gamma function*, J. Approx. Theory**40**(1984), no. 2, 115–120. MR**732692**, https://doi.org/10.1016/0021-9045(84)90020-0**[5]**G. N. Watson,*A note on Gamma functions*, Proc. Edinburgh Math. Soc. (2)**11**(1958/1959), no. Edinburgh Math. Notes 42 (misprinted 41) (1959), 7–9. MR**0117358**

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

Article copyright:
© Copyright 1984
American Mathematical Society