Results 311 to 320 of about 12,298,354 (363)
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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
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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
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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
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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
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On gamma function inequalities
Scandinavian Actuarial Journal, 1973Watson's method [1] is used to find two convergent monotonically non-decreasing sequences whose upper bounds are equal to Γ(l)Γ(l∓2a)/Γ2(l∓a) ( = K say), provided l > max (0, - 2a). Boyd [2] showed that Gurland's inequality [3] for K corresponds to the first term of the first sequence; Raja Rao's inequality [4] corresponds to the second term of the ...
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An Inequality for Gamma Functions
Canadian Mathematical Bulletin, 1978By using Bellman-Wishart distribution, Bellman [1], an inequality for gamma functions is derived. This inequality generalizes a recent inequality given by Selliah [4].
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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.
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Canadian Journal of Mathematics, 1954
The gamma function Γ(z + 1) = П(z) has been defined in different ways:(1)(Weierstrass)(2)(Kuler)(3)(Gauss)(4)(Euler)(5)(Lerch)
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The gamma function Γ(z + 1) = П(z) has been defined in different ways:(1)(Weierstrass)(2)(Kuler)(3)(Gauss)(4)(Euler)(5)(Lerch)
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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
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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
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1998
The problem of extending the function n! to real arguments and finding the simplest possible “factorial function” with value n! at n ∈ ℕ led Euler in 1729 to the Г-function. He gave the infinite product $$\Gamma \left( {z + 1} \right): = \frac{{1 \cdot {2^z}}}{{1 + z}} \cdot \frac{{{2^{1 - z}}{3^z}}}{{2 + z}} \cdot \frac{{{3^{1 - z}}{4^z}}}{{3 + z}}
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The problem of extending the function n! to real arguments and finding the simplest possible “factorial function” with value n! at n ∈ ℕ led Euler in 1729 to the Г-function. He gave the infinite product $$\Gamma \left( {z + 1} \right): = \frac{{1 \cdot {2^z}}}{{1 + z}} \cdot \frac{{{2^{1 - z}}{3^z}}}{{2 + z}} \cdot \frac{{{3^{1 - z}}{4^z}}}{{3 + z}}
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On an inequality for gamma functions
Scandinavian Actuarial Journal, 1962Abstract For all real values of α and λ satisfying the following inequality holds. When compared with a similar inequality due to Gurland [3] this is seen to be stronger for a certain range of α.
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