منابع مشابه
Convenient formulae for some integrals in perturbation theory
The free energy and pressure of a fluid, as given by perturbation theory, involve integrals of the hard sphere correlation functions and their density derivatives. In most applications a straightforward procedure would be to obtain these integrals, possibly numerically, using the formulae and computer codes for the hard sphere correlation functions, given previously [Mol. Phys., 2007, 106, 2; C...
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We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialization of the results he...
متن کاملIntegrals involving complete elliptic integrals
We give a closed-form evaluation of a number of Erd elyi-Kober fractional integrals involving elliptic integrals of the rst and second kind, in terms of the 3F2 generalized hypergeometric function. Reduction formulae for 3F2 enable us to simplify the solutions for a number of particular cases. c © 1999 Elsevier Science B.V. All rights reserved.
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چکیده ندارد.
15 صفحه اولElliptic Approximations of Propositional Formulae
A propositional formula can be approximated by a concave quadratic function. This approximation is obtained as a second order Taylor expansion of a convex smooth model. It is shown that in the 3-SAT case, the involved parameters can be set to such values that yield optimal discriminative properties. Two concentric (generally elliptic) quadratic convex regions are established, the inner one cont...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1877
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01444647