Results 51 to 60 of about 5,444,686 (168)

Some properties of the psi and polygamma functions

, 2009
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
GUO, Bai-ni, Qİ, Feng
openaire   +3 more sources

Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions [PDF]

Mathematical Problems in Engineering, 2020
In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function.
Fuli He, Ahmed Bakhet, Mohamed Akel, Mohamed Abdalla   +3 more
openaire   +2 more sources

Sharp Generalized Inequalities for Certain Finite Products Derived From Complete Monotonicity and the Gamma Function

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we establish a unified approach of inequalities for the finite products (i · (i + k) · ⋅⋅(i + (n − 1)k))/(k · 2k · ⋅⋅(nk)), where k ≥ 2 is a fixed integer and i ∈ {1, 2, …, k − 1}. Motivated by previously known results for the cases k = 2, 3, 4, and 5, we express these products in terms of gamma function ratios and investigate the ...
Jenică Crînganu, Smritijit Sen
wiley   +1 more source

Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Mathematics, 2019
In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite⁻Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex.
Shilpi Jain, Khaled Mehrez, Dumitru Baleanu, Praveen Agarwal   +3 more
doaj   +1 more source

SOME COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND POLYGAMMA FUNCTIONS [PDF]

Journal of the Korean Mathematical Society, 2008
Summary: Some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.
Li, Ai-Jun, Chen, Chao-Ping
openaire   +1 more source

Fractional Q$Q$‐curvature on the sphere and optimal partitions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara, Juan Carlos Fernández, Alberto Saldaña   +2 more
wiley   +1 more source

The Best Bounds in Gautschi-Kershaw Inequalities [PDF]

, 2005
By employing the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma, psi and polygamma functions, and other analytic techniques, this note provides an alternative proof of a monotonicity and ...
Qi, Feng, Chao-Ping Chen, Chen, Chao-Ping, Feng Qi, Bai-Ni Guo, Guo, Bai-Ni   +5 more
core   +3 more sources

Families of skew linear harmonic Euler sums involving some parameters

Cubo
In this study we investigate a family of skew linear harmonic Euler sums involving some free parameters. Our analysis involves using the properties of the polylogarithm function, commonly referred to as the Bose-Einstein integral.
Anthony Sofo
doaj   +1 more source

Estimation and Inference for Higher‐Order Stochastic Volatility Models With Leverage

Journal of Time Series Analysis, Volume 46, Issue 6, Page 1064-1084, November 2025.
ABSTRACT Statistical inference—estimation and testing—for stochastic volatility models is challenging and computationally expensive. This problem is compounded when leverage effects are allowed. We propose efficient, simple estimators for higher‐order stochastic volatility models with leverage [SVL(p)$$ (p) $$], based on a small number of moment ...
Md. Nazmul Ahsan, Jean‐Marie Dufour, Gabriel Rodriguez‐Rondon   +2 more
wiley   +1 more source

Parameterized Finite Binomial Sums

Mathematics
We offer intriguing new insights into parameterized finite binomial sums, revealing elegant identities such as ∑k=0,k≠nm+n(−1)kn−km+nk=(−1)nm+nn(Hm−Hn), where n,m are non-negative integers and Hn is the harmonic number. These formulas beautifully capture
Necdet Batır, Junesang Choi
doaj   +1 more source