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Some Properties on the Function Involving the Gamma Function

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DOI: 10.4236/am.2012.36090    6,283 Downloads   8,498 Views   Citations
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ABSTRACT

We studied the monotonicity and Convexity properties of the new functions involving the gamma function, and get the general conclusion that Minc-Sathre and C. P. Chen-G. Wang’s inequality are extended and refined.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Chen, "Some Properties on the Function Involving the Gamma Function," Applied Mathematics, Vol. 3 No. 6, 2012, pp. 587-589. doi: 10.4236/am.2012.36090.

References

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[3] F. Qi, “Inequalities and Monotonicity of Sequences Involving ,” Soochow Journal of Mathematics, Vol. 29, No. 4, 2003, pp. 353-361.
[4] F. Qi and Q.-M. Luo, “Generalization of H. Minc and J. Sathre’s Inequality,” Tamkang Journal of Mathematics, Vol. 31, No. 2, 2000, pp. 145-148.
[5] D. Kershaw and A. Laforgia, “Monotonicity Results for the Gamma Function,” Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., Vol. 119, 1985, pp. 127-133.
[6] C.-P. Chen and G. Wang, “Monotonicity and Logarithmic Convexity Properties for the Gamma Function,” Scientia, Vol. 5, No. 1, 2009, pp. 51-54.
[7] M. Abramowitz and I. A. Stegun (Eds.), “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards,” Applied Mathematics Series, 4th Printing, Washington, Vol. 55, 1965.

  
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