Journal ArticleDOI
Integral representation of some functions related to the Gamma function
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In this paper, it was shown that the functions Θ(Θ(x) = [Gamma (x + 1)]^{1/x} (1 + 1/x)^x /x) and Θ (Θ (x, Θ) = Θ((Θ + 1)/x)) are Stieltjes transforms.Citations
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Characterizations of real hypersurfaces of type a in a complex space form
U-Hang Ki,In-Bae Kim,Dong Ho Lim +2 more
TL;DR: In this article, it was shown that if R»L»g = 0 holds on M, then M is a Hopf hypersurface in Mn(c), where R and L» denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field respectively.
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New Integral representations for the Fox-Wright functions and its applications
Khaled Mehrez,Khaled Mehrez +1 more
TL;DR: In this article, closed-form integral expressions for the Fox-Wright function under a special restriction on parameters were derived for the four parameter Wright function under the assumption of complete monotonicity property.
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The reciprocal of the weighted geometric mean is a Stieltjes function
Feng Qi,Feng Qi,Bai-Ni Guo +2 more
TL;DR: In this article, the authors derived that the reciprocal of the weighted geometric mean of two positive numbers is a Stieltjes function and consequently a (logarithmically) completely monotonic function.
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Some properties of the Schröder numbers
Feng Qi,Xiao-Ting Shi,Bai-Ni Guo +2 more
TL;DR: In this article, the authors present some properties of the large Schroder numbers, including convexity, complete monotonicity, product inequalities, and determinantal inequalities and find three relations between the Schroder number and the central Delannoy number.
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A function involving gamma function and having logarithmically absolute convexity
TL;DR: In this paper, the logarithmically complete monotonicity, log-arithmic absolute convexity of the function [Γ(1+tx)] s /[Γ (1+sx)] t for x, s, t∈ℝ such that 1+ sx>0 and 1+tx>0 with s≠t are verified, some known results are generalized.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
A table of integrals
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions