Some properties of the Catalan-Qi function related to the Catalan numbers
被引:26
|
作者:
Qi, Feng
论文数: 0引用数: 0
h-index: 0
机构:
Henan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China
Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China
Tianjin Polytech Univ, Dept Math, Sch Sci, Tianjin 300387, Peoples R ChinaHenan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China
Qi, Feng
[1
,2
,4
]
Mahmoud, Mansour
论文数: 0引用数: 0
h-index: 0
机构:
Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, EgyptHenan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China
Mahmoud, Mansour
[3
]
Shi, Xiao-Ting
论文数: 0引用数: 0
h-index: 0
机构:
Tianjin Polytech Univ, Dept Math, Sch Sci, Tianjin 300387, Peoples R ChinaHenan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China
Shi, Xiao-Ting
[4
]
Liu, Fang-Fang
论文数: 0引用数: 0
h-index: 0
机构:
Tianjin Polytech Univ, Dept Math, Sch Sci, Tianjin 300387, Peoples R ChinaHenan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China
Liu, Fang-Fang
[4
]
机构:
[1] Henan Polytech Univ, Inst Math, Jiaozuo City 454010, Henan Province, Peoples R China
[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China
[3] Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, Egypt
[4] Tianjin Polytech Univ, Dept Math, Sch Sci, Tianjin 300387, Peoples R China
来源:
SPRINGERPLUS
|
2016年
/
5卷
关键词:
Property;
Catalan number;
Catalan function;
Catalan-Qi function;
Asymptotic expansion;
Integral representation;
Logarithmic convexity;
Complete monotonicity;
Logarithmically complete monotonicity;
Minimality;
Inequality;
Ratio of gamma functions;
COMPLETE MONOTONICITY;
D O I:
10.1186/s40064-016-2793-1
中图分类号:
O [数理科学和化学];
P [天文学、地球科学];
Q [生物科学];
N [自然科学总论];
学科分类号:
07 ;
0710 ;
09 ;
摘要:
In the paper, the authors find some properties of the Catalan numbers, the Catalan function, and the Catalan-Qi function which is a generalization of the Catalan numbers. Concretely speaking, the authors present a new expression, asymptotic expansions, integral representations, logarithmic convexity, complete monotonicity, minimality, logarithmically complete monotonicity, a generating function, and inequalities of the Catalan numbers, the Catalan function, and the Catalan-Qi function. As by-products, an exponential expansion and a double inequality for the ratio of two gamma functions are derived.