k-Gama Fonksiyonu Üzerine Bazı Monotonluk Özellikleri

Yıl 2019, Cilt: 9 Sayı: 1, 66 - 76, 28.06.2019

Emrah Yıldırım , İnci Ege

Öz

Bu
çalışmanın amacı,  olmak
üzere -gama fonksiyonunun logaritmasını içeren
bazı fonksiyonların monotonluk özelliklerini elde etmektir.

Anahtar Kelimeler

k-Gama fonksiyonu, Monotonluk, k-Poligama fonksiyonu

Some Monotonicity Properties on k-Gamma Function

Öz

The aim of this work is to obtain some monotonicity properties for the
functions involving the logarithms of the k



















-gamma function for

k>0.

Anahtar Kelimeler

k-Gamma function, Monotonicity, k-Polygamma function

Kaynakça

• Abramowitz M., Stegun I. A., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
• Alzer H., Some gamma function inequalities, Math. Comp., 60, 337-346, 1993.
• Alzer H., Inequalities for the gamma and psi functions, Abh. Math. Sem. Hamburg, 68, 363-372, 1998.
• Anderson, G., Qiu, S. L., A monotoneity property of the gamma function, Proceedings of the American Mathematical Society, 125(11), 3355-3362, 1997.
• Diaz R., Pariguan E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15(2), 179-192, 2007.
• Elbert, Á., Laforgia, A., On some properties of the gamma function, Proceedings of the American Mathematical Society, 128(9), 2667-2673, 2000.
• Gautschi W., Some elementary inequalities relating to the gamma and incomplete gamma function, Journal of Mathematics and Physics, 38(1), 77-81, 1959.
• Gradshteyn, I. S., Ryzhik, I. M. Table of integrals, series, and products. Academic press, 2014.
• Krasniqi V., Inequalities and monotonicity for the ration of k-gamma function, Scientia Magna, 6(1), 40-45, 2010.
• Neumann E., Some inequalities for the gamma function, Appl. Math. Comput., 218(8), 4349-4352, 2011.
• Sandor, J., Sur la fonction Gamma, Publ. C. Rech. Math. Pures Neuchâtel, 4-7, 1989.