For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1. Then P(Xa−a\u3ec) is increasing in a for each real c⩾0; non-increasing in a for each real c⩽−1∕3; and non-monotonic in a for each c∈(−1∕3,0). This extends and/or refines certain previously established results
We give an infinite family of functions involving the gamma function whose logarithmic derivatives a...
AbstractThree new properties are derived. The first one relates to the distribution ofUG+G′, where t...
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
AbstractLet Gc(x)=logΓ(x)−xlogx+x−12log(2π)+12ψ(x+c)(x>0;c≥0). We prove that Ga is completely monoto...
We denote by Γ(a) and Γ(a;z) the gamma and the incomplete gamma functions, respec-tively. In this pa...
AbstractThe gamma function and its various modifications such as the (upper) incomplete, regularized...
Let Y be a standard Gamma(k) distributed random variable (rv), k > 0, and let X be an independent...
AbstractSeveral functions involving the gamma function Γ(x) and the q-gamma function Γq(x) are prove...
Let Y be a standard Gamma(k) distributed random variable (rv), k > 0, and let X be an independent...
In this paper we analyze the monotony of the function ln Γ(x)ln (x2+τ)-ln (x+τ)${{{\rm{ln}}\,\Gamma...
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonic...
We prove some properties of completely monotonic functions and apply them to obtain new results on ...
The symmetric patterns that inequalities contain are reflected in researchers’ studies in many mathe...
We give an infinite family of functions involving the gamma function whose logarithmic derivatives a...
AbstractThree new properties are derived. The first one relates to the distribution ofUG+G′, where t...
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
For real a\u3e0, let Xa denote a random variable with the gamma distribution with parameters a and 1...
AbstractLet Gc(x)=logΓ(x)−xlogx+x−12log(2π)+12ψ(x+c)(x>0;c≥0). We prove that Ga is completely monoto...
We denote by Γ(a) and Γ(a;z) the gamma and the incomplete gamma functions, respec-tively. In this pa...
AbstractThe gamma function and its various modifications such as the (upper) incomplete, regularized...
Let Y be a standard Gamma(k) distributed random variable (rv), k > 0, and let X be an independent...
AbstractSeveral functions involving the gamma function Γ(x) and the q-gamma function Γq(x) are prove...
Let Y be a standard Gamma(k) distributed random variable (rv), k > 0, and let X be an independent...
In this paper we analyze the monotony of the function ln Γ(x)ln (x2+τ)-ln (x+τ)${{{\rm{ln}}\,\Gamma...
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonic...
We prove some properties of completely monotonic functions and apply them to obtain new results on ...
The symmetric patterns that inequalities contain are reflected in researchers’ studies in many mathe...
We give an infinite family of functions involving the gamma function whose logarithmic derivatives a...
AbstractThree new properties are derived. The first one relates to the distribution ofUG+G′, where t...
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove...
DOI
Add to ORKG