Some New Inequalities for Gamma and Polygamma Functions

2004

71 citations recorded by the source corpus.

Citations in the corpus

On some properties of digamma and polygamma functions (2007, unknown): “In [13, Theorem 2.1(b)] the author of this paper proved that lim x →∞ θ 0 (x) = 1 / 2.”
A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application (2006, unknown): “in{s,t}. In [3, p. 208], [8, Lemma 1.1] and [9, Lemma 1.1], the inequality ∆0,0(x) = [ψ ′(x)]2 +ψ′′(x) >0 (13) A CLASS OF COMPLETELY MONOTONIC FUNCTIONS AND APPLICATIONS 3 on (0,∞) was veriﬁed. In [4, 8, 9], this inequality was applied to provide some symmetrical upper and lower bounds for Γ(x) i”
Bounds for the Ratio of Two Gamma Functions (2009, unknown): “In [28], the authors investigated some general cases seemingly related with the ratio of two gamma functions but essentially similar to the f -means in [44] and some results appeared in [16, 17, 18].”
Inequalities for the gamma function (2008, unknown): “In [12] it was proved that lim x→∞ [x− e] = 1/2.”