scholarly journals THE q-DEFORMED GAMMA FUNCTION AND q-DEFORMED POLYGAMMA FUNCTION

2014 ◽  
Vol 51 (4) ◽  
pp. 1155-1161 ◽  
Author(s):  
Won Sang Chung ◽  
Taekyun Kim ◽  
Toufik Mansour
Keyword(s):  
Gamma Function ◽  
Polygamma Function

Completely monotonic functions related to the q-gamma and the q-trigamma functions

2015 ◽  
Vol 13 (02) ◽  
pp. 125-134 ◽  
Author(s):  
Ahmed Salem
Keyword(s):  
Gamma Function ◽  
Infinite Class ◽  
Positive Real ◽  
Digamma Function ◽  
Sharp Bounds ◽  
Monotonic Functions ◽  
Polygamma Function ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

In this paper, two completely monotonic functions involving the q-gamma and the q-trigamma functions where q is a positive real, are introduced and exploited to derive sharp bounds for the q-gamma function in terms of the q-trigamma function. These results, when letting q → 1, are shown to be new. Also, sharp bounds for the q-digamma function in terms of the q-tetragamma function are derived. Furthermore, an infinite class of inequalities for the q-polygamma function is established.

HÖLDER-TYPE INEQUALITIES FOR THE POLYGAMMA FUNCTIONS

2008 ◽  
Vol 06 (02) ◽  
pp. 113-119
Author(s):  
HORST ALZER
Keyword(s):  
Gamma Function ◽  
Real Numbers ◽  
Polygamma Function ◽  
Polygamma Functions

The nth polygamma function is defined by ψ(n) = (Γ′/Γ)(n), where Γ denotes Euler's gamma function. We prove: let n ≥ 1 be an integer and let p, q be non-zero real numbers. (i) The inequality [Formula: see text] holds for all positive numbers x, y if and only if p > 0, q > 0, 1/p + 1/q ≥ 1. (ii) The inequality [Formula: see text] holds for all positive numbers x, y if and only if either p < 0, q < 0 or pq < 0, 1/p + 1/q ≤ 1.

ON THE INCOMPLETE GAMMA FUNCTION AND ITS NEUTRIX CONVOLUTION FOR NEGATIVE INTEGERS

2019 ◽  
Vol 10 (1) ◽  
pp. 30-51
Author(s):  
Mongkolsery Lin ◽  
◽  
Brian Fisher ◽  
Somsak Orankitjaroen ◽  
◽  
...  
Keyword(s):  
Gamma Function ◽  
Incomplete Gamma Function

Gamma Function and Its Functional Equations

Resonance ◽  
2021 ◽  
Vol 26 (3) ◽  
pp. 367-386
Author(s):  
Ritesh Goenka ◽  
Gopala Krishna Srinivasan
Keyword(s):  
Gamma Function ◽  
Functional Equations

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
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