The best bounds in Gautschi-Kershaw inequalities

Qi, Feng; Guo, Bai‐Ni; Chen, Chao-Ping

doi:10.7153/mia-09-41

Cited by 38 publications

(49 citation statements)

References 15 publications

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“…please see the papers [14,15,17,33,36,37,38,41,42,43,48,44,47,54,55], the expository and survey articles [34,35,45,46], and a number of references cited therein. In 2011, Batir [5,Theorem 2.7] obtained the double inequality 4) where the constants a * = 1 2 and b * = π 2 6e 2γ = 0.518 .…”

Section: Motivations and Main Resultsmentioning

confidence: 99%

Some inequalities for the trigamma function in terms of the digamma function

Mortici

2015

Applied Mathematics and Computation

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Abstract. In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The method in the paper utilizes some facts from the asymptotic theory and is a natural way to solve problems for approximating some quantities for large values of the variable. Motivations and main resultsThe classical Euler gamma function may be defined for ℜ(z) > 0 byThe logarithmic derivative of the gamma function Γ(z) is denoted byand called the digamma function. The derivatives ψ ′ (z) and ψ ′′ (z) are called the trigamma and tetragamma functions respectively. As a whole, the functions ψ (k) (z) for k ∈ {0}∪N are called the polygamma functions. These functions are widely used in theoretical and practical problems in all branches of mathematical science. Consequently, many mathematicians were preoccupied to establish new results about the gamma function, polygamma functions, and other related functions.

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Section: Motivations and Main Resultsmentioning

confidence: 99%

Some inequalities for the trigamma function in terms of the digamma function

Mortici

2015

Applied Mathematics and Computation

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“…Some related references are listed in [2,3,4,5,6,15,23,41]. In recent years, inequalities and (logarithmically) completely monotonic functions involving the gamma, psi, or polygamma functions are established by some mathematicians (see [2,3,4,11,15,17,21,31] and related references therein).…”

Section: ∞) This Tells Us That F ∈ C[[0 ∞)] If and Only If It Is mentioning

confidence: 99%

Some Logarithmically Completely Monotonic Functions Related to the Gamma Function

Qi¹,

Guo²

2010

Journal of the Korean Mathematical Society

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“…For more information on the logarithmically completely monotonic functions defined by Definition 2, please refer to [4,5,8,11,12,13], especially [7,10,15], and the references therein.…”

Section: Definitionmentioning

confidence: 99%