scholarly journals Monotonicity Properties Related to the Ratio of Two Gamma Functions

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Nian Hong Zhou ◽  
Da-Wei Niu
Keyword(s):  
Gamma Functions ◽  
Monotonicity Properties

scholarly journals Logarithmically complete monotonicity and Shur-convexity for some ratios of gamma functions

2006 ◽  
pp. 88-92 ◽  
Author(s):  
Li Ai-Jun ◽  
Zhao Wei-Zhen ◽  
Chen Chao-Ping
Keyword(s):  
Complete Monotonicity ◽  
Gamma Functions ◽  
Monotonicity Properties ◽  
Schur Convex

Define F(x) = ?(mx) xm-1?m(x) and G(x)- ?(mx) ?m(x). for x > 0 and m = 2 3,?. In this paper, we consider the logarithmically complete monotonicity properties for the function F and 1/G, and we prove that the function ?(x) = ? n i=1 ?(mxi + 1) ?m (x1 + 1) is strictly Schur-convex (-1/m,+?)n.

scholarly journals Some Monotonicity Properties of Gamma and q-Gamma Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Peng Gao
Keyword(s):  
Gamma Functions ◽  
Monotonicity Properties

We prove some monotonicity properties of functions involving gamma and q-gamma functions.

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

Some complete monotonicity properties for the -gamma function

2013 ◽  
Vol 219 (21) ◽  
pp. 10538-10547 ◽  
Author(s):  
V.B. Krasniqi ◽  
H.M. Srivastava ◽  
S.S. Dragomir
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Monotonicity Properties

Monotonicity Properties of Determinants of Special Functions

2006 ◽  
Vol 26 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Mourad E.H. Ismail ◽  
Andrea Laforgia
Keyword(s):  
Special Functions ◽  
Monotonicity Properties
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