Research Article
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Year 2019, , 104 - 111, 01.01.2019
https://doi.org/10.18038/aubtda.438249

Abstract

References

  • Gautschi W. Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959; 38-1: 77-81.
  • Neuman E. Some inequalities for the gamma function. Appl. Math. Comput. 2011; 218-8: 4349-4352.
  • Diaz R, Pariguan E. On hypergeometric functions and Pachhammer k-symbol. Divulg. Mat. 2007; 15-2: 179-192.
  • Krasniqi V. Inequalities and monotonicity for the ration of k -gamma function. Scientia Magna. 2010; 6-1: 40-45.
  • Gradshteyn, I. S., Ryzhik, I. M. Table of integrals, series, and products. Academic Press, 2014.

MONOTONICITY RESULTS AND ASSOCIATED INEQUALITIES FOR K-GAMMA FUNCTION

Year 2019, , 104 - 111, 01.01.2019
https://doi.org/10.18038/aubtda.438249

Abstract

In this work, we find-analogue of Gautschi inequality and obtain some monotonicity results for-gamma function. By the aid of these, we also get some more inequalities.

This study is inspired bythe work of Neumann in 2011. In the study, weestablish some double inequalities involving the ratio𝛤𝑘(𝑛+𝑠)𝛤𝑘(𝑛+𝑘), where 𝛤𝑘is the 𝑘-analogue of Euler’s gamma function. Some monotonicity results involvingk-gamma functionare found. By the aid of these results, some inequalitiessuchas[Γ𝑘(𝑘+𝜎)]𝑘𝜎≤∑[Γ𝑘(𝑘+𝑥𝑖)]𝑘𝑥𝑖𝑛𝑖=1for 𝑥𝑖>0, 1≤𝑖≤𝑛, where 𝜎=𝑥1+𝑥2+⋯+𝑥𝑛are valid.

References

  • Gautschi W. Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959; 38-1: 77-81.
  • Neuman E. Some inequalities for the gamma function. Appl. Math. Comput. 2011; 218-8: 4349-4352.
  • Diaz R, Pariguan E. On hypergeometric functions and Pachhammer k-symbol. Divulg. Mat. 2007; 15-2: 179-192.
  • Krasniqi V. Inequalities and monotonicity for the ration of k -gamma function. Scientia Magna. 2010; 6-1: 40-45.
  • Gradshteyn, I. S., Ryzhik, I. M. Table of integrals, series, and products. Academic Press, 2014.
There are 5 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İnci Ege 0000-0002-3702-7456

Emrah Yıldırım 0000-0002-4563-5275

Publication Date January 1, 2019
Published in Issue Year 2019

Cite

AMA Ege İ, Yıldırım E. MONOTONICITY RESULTS AND ASSOCIATED INEQUALITIES FOR K-GAMMA FUNCTION. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. January 2019;20(1):104-111. doi:10.18038/aubtda.438249