Some Properties on the Function Involving the Gamma Function

Author(s)
Bin Chen

Affiliation(s)

Department of Mathematics and Information Science, Weinan Normal University, Shaanxi, China.

Department of Mathematics and Information Science, Weinan Normal University, Shaanxi, China.

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.

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.

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.

B. Chen, "Some Properties on the Function Involving the Gamma Function,"

References

[1] H. Minc and L. Sathre, “Some Inequalities Involving ,” Proceedings of the Edinburgh Mathematical Society, Vol. 14, No. 65, 1964, pp. 41-46. doi:10.1017/S0013091500011214

[2] B.-N. Guo and F. Qi, “Inequalities and Monotonicity for the Ratio of Gamma Functions,” Taiwanese Journal of Mathematics, Vol. 7, No. 2, 2003, pp. 239-247.

[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.

[1] H. Minc and L. Sathre, “Some Inequalities Involving ,” Proceedings of the Edinburgh Mathematical Society, Vol. 14, No. 65, 1964, pp. 41-46. doi:10.1017/S0013091500011214

[2] B.-N. Guo and F. Qi, “Inequalities and Monotonicity for the Ratio of Gamma Functions,” Taiwanese Journal of Mathematics, Vol. 7, No. 2, 2003, pp. 239-247.

[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.