Results 291 to 300 of about 1,274,911 (326)
Some of the next articles are maybe not open access.
2004
We have defined (Set Theory, III, p. 179) the function n! for every integer n ≥ 0, as equal to the product \(\prod\limits_{0 \leqslant k \leqslant n} {(n - k)}\); so 0!=1 and (n+1)!=(n+1)n! for n ≥ 0. We set г(n) = (n − 1)! for each integer n ≥ 1; we propose to define, on the set of real numbers x > 0, a continuous function г(x) extending the function ...
Elementary Theory, Philip Spain
openaire +2 more sources
We have defined (Set Theory, III, p. 179) the function n! for every integer n ≥ 0, as equal to the product \(\prod\limits_{0 \leqslant k \leqslant n} {(n - k)}\); so 0!=1 and (n+1)!=(n+1)n! for n ≥ 0. We set г(n) = (n − 1)! for each integer n ≥ 1; we propose to define, on the set of real numbers x > 0, a continuous function г(x) extending the function ...
Elementary Theory, Philip Spain
openaire +2 more sources
2012
In what follows, we introduce the classical Gamma function in Sect. 2.1. It is essentially understood to be a generalized factorial. However, there are many further applications, e.g., as part of probability distributions (see, e.g., Evans et al. 2000).
Willi Freeden, Martin Gutting
openaire +2 more sources
In what follows, we introduce the classical Gamma function in Sect. 2.1. It is essentially understood to be a generalized factorial. However, there are many further applications, e.g., as part of probability distributions (see, e.g., Evans et al. 2000).
Willi Freeden, Martin Gutting
openaire +2 more sources
Inequalities for the gamma function
Archiv der Mathematik, 2008Some inequalities for the gamma function are given. These results refine the classical Stirling approximation and its many recent improvements.
openaire +3 more sources
The Gamma Function and the Incomplete Gamma Functions
2017The gamma function is defined for \(s \in \mathbb{C}\) by $$\displaystyle{ \varGamma \left (s\right ) =\int _{ 0}^{\infty }t^{s-1}e^{-t}dt }$$
openaire +2 more sources
The Gamma Functional Navigator
IEEE Transactions on Nuclear Science, 2004We have developed a new device that allows precise guided surgery through gamma-camera images in real time. It consists of a portable mini gamma camera combined with an image guided surgery system. We call this new instrument the "Gamma Functional Navigator." The small gamma camera has been built by our group and has a spatial resolution of about 2 mm.
J.L. Palmero +12 more
openaire +2 more sources
Integral representations for the Gamma function, the Beta function, and the Double Gamma function
Integral Transforms and Special Functions, 2009A variety of integral representations for some special functions have been developed. Here we aim at presenting certain (new or known) integral representations for , B(α, β), and by using some of the known integral representations of the Hurwitz (or generalized) Zeta function ζ(s, a).
Junesang Choi, Hari M. Srivastava
openaire +2 more sources
The Gamma and Zeta Functions [PDF]
, 1993 We now come to a situation where the natural way to define a function is not through a power series but through an integral depending on a parameter. We shall give a natural condition when we can differentiate under the integral sign, and we can then use Goursat’s theorem to conclude that the holomorphic function so defined is analytic.
openaire +1 more source
Multiple Gamma and related functions
Applied Mathematics and Computation, 2003The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical definite integral due to Euler and other definite integrals are also considered together with closed-form evaluations of some series involving
Hari M. Srivastava +2 more
openaire +2 more sources
The Gamma Function and Related Functions
1998Abstract Because it is a generalization of n!, the gamma function has been examined over the years as a means of generalizing certain functions, operations, etc., that are commonly defined in terms of factorials. In addition, the gamma function is useful in the evaluation of many nonelementary integrals and in the definition of other ...
openaire +2 more sources
A FUNCTIONAL INEQUALITY FOR THE GAMMA FUNCTION
Analysis and Applications, 2013Let α and β be real numbers. We prove that the functional inequality [Formula: see text] holds for all positive real numbers x and y if and only if [Formula: see text] Here, γ denotes Euler's constant.
openaire +2 more sources