Results 31 to 40 of about 513 (70)
A completely monotonic function involving the tri- and tetra-gamma functions
, 2010 The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function.
Guo, Bai-Ni, Qi, Feng
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Certain Inequalities Involving the $q$-Deformed Gamma Function
, 2014 This paper is inspired by the work of J. S\'{a}ndor in 2006. In the paper, the authors establish some double inequalities involving the ratio $ \frac{\Gamma_{q}(x+1)}{ \Gamma_{q} \left( x+\frac{1}{2}\right)}$, where $\Gamma_{q}(x)$ is the $q$-deformation
Nantomah, Kwara, Prempeh, Edward
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Some completely monotonic functions involving the polygamma functions [PDF]
, 2010 Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.Comment: 6 ...
Gao, Peng
core
Solution to an open problem on a logarithmic integral and derived results
Annals of the West University of Timisoara: Mathematics and Computer ScienceThis article solves an open problem that was previously stated by providing an exact evaluation of a logarithmic integral. Furthermore, the result is generalized by introducing a new adjustable parameter.
Coine Clément, Chesneau Christophe
doaj +1 more source
On Solving Some Trigonometric Series [PDF]
, 2013 This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function.
Stenlund, Henrik
core
, 2018 Let $d\in \mathbb{N}$ and let $\gamma_i\in [0,\infty)$, $x_i\in (0,1)$ be such that $\sum_{i=1}^{d+1} \gamma_i = M\in (0,\infty)$ and $\sum_{i=1}^{d+1} x_i = 1$.
Ouimet, Frédéric
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On the Power Series Expansion of the Reciprocal Gamma Function [PDF]
, 2017 Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values of the indices.
Fekih-Ahmed, Lazhar
core
Sharp bounds for harmonic numbers
, 2010 In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double ...
Alzer +23 more
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Further extension of the generalized Hurwitz-Lerch Zeta function of two variables
, 2019 The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with generalized ...
Nisar, Kottakkaran Sooppy
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Some special functions identities arising from commuting operators
, 2008 Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of order $k$ and the
Abramowitz +8 more
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