scholarly journals Complete Monotonicity Properties of a Function Involving the Polygamma Function

2018 ◽  
Vol 1(2018) (1) ◽  
pp. 10-15
Author(s):  
Kwara Nantomah ◽  
Keyword(s):  
Complete Monotonicity ◽  
Polygamma Function ◽  
Monotonicity Properties

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

scholarly journals Sharp Inequalities for Polygamma Functions

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Bai-Ni Guo ◽  
Feng Qi ◽  
Jiao-Lian Zhao ◽  
Qiu-Ming Luo
Keyword(s):  
Rational Functions ◽  
Complete Monotonicity ◽  
Double Inequality ◽  
Polygamma Function ◽  
Polygamma Functions

AbstractIn the paper, the authors review some inequalities and the (logarithmically) complete monotonicity concerning the gamma and polygamma functions and, more importantly, present a sharp double inequality for bounding the polygamma function by rational functions.

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 Logarithmically complete monotonicity properties and characterizations of the gamma function

2007 ◽  
Vol 38 (4) ◽  
pp. 313-322
Author(s):  
Ai-Jun Li ◽  
Chao-Ping Chen
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Monotonicity Properties ◽  
Monotonic Properties

n this paper, the logarithmically complete monotonic properties of the functions $ \prod_{i=1}^{n}\frac{\Gamma(x-a_i)}{\Gamma(x-b_i)} $ ,$ \Gamma(x)^{\alpha}\Gamma\Big(x-\sum_{i=1}^n a_i\Big)/\prod_{i=1}^{n}\Gamma(x-a_i) $, and $ x^r(e/x)^x \Gamma(x) $ are obtained. Some characterizations of the gamma function are deduced.

scholarly journals On modifications of the exponential integral with the Mittag-Leffler function

2018 ◽  
Vol 21 (5) ◽  
pp. 1156-1169 ◽  
Author(s):  
Francesco Mainardi ◽  
Enrico Masina
Keyword(s):  
Time Domain ◽  
Linear Viscoelasticity ◽  
Special Function ◽  
Complete Monotonicity ◽  
Exponential Integral ◽  
Monotonicity Properties ◽  
The Time Domain

Abstract In this paper we survey the properties of the Schelkunoff modification of the Exponential integral and we generalize it with the Mittag-Leffler function. So doing we get a new special function (as far as we know) that may be relevant in linear viscoelasticity because of its complete monotonicity properties in the time domain. We also consider the generalized sine and cosine integral functions.

scholarly journals Logarithmically Complete Monotonicity Properties Relating to the Gamma Function

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Tie-Hong Zhao ◽  
Yu-Ming Chu ◽  
Hua Wang
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Completely Monotonic ◽  
Monotonicity Properties

We prove that the functionfα,β(x)=Γβ(x+α)/xαΓ(βx)is strictly logarithmically completely monotonic on(0,∞)if(α,β)∈{( α,β):1/α≤β≤1, α≠1}∪{(α,β):0<β≤1,φ1(α,β)≥0,φ2(α,β)≥0}and[fα,β(x)]-1is strictly logarithmically completely monotonic on(0,∞)if(α,β)∈{(α,β):0<α≤1/2,0<β≤1}∪{(α,β):1≤β≤1/α≤2,α≠1}∪{(α,β):1/2≤α<1,β≥1/(1-α)}, whereφ1(α,β)=(α2+α-1)β2+(2α2-3α+1)β-αandφ2(α,β)=(α-1)β2+(2α2-5α+2)β-1.

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