منابع مشابه
The Tabulation of Mathieu Functions
and in which a and 6 are constants, arises in applied mathematics in two main groups of problems. The first group, of which Mathieu's problem of the transverse vibrations of a taut elliptic membrane is typical, consists of boundary problems relative to some partial differential equation, such as the wave equation, where the boundary is an ellipse—or possibly a hyperbola. Here a fundamental requ...
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An extended version of the applicative caching technique from functional programming is adapted to OLD resolution as an alternative to OLDT resolution for predicates that are actually functions. An inference system, OLDTF resolution, is given with a proof procedure. It is argued why this special case is interesting in its own right also outside the area of deductive databases. It is outlined ho...
متن کاملTabulation of the Functions ^-7^- , v = ±è
(1) f ddK0(2zcosd) cos(2„É>) = -í/j_(*)Í.J,(«) + L(z) £-/-,(*)); Jo 4 ^ oV oV J where 7f0 denotes a modified Bessel function of the second kind. Oberhettinger [2] has previously discussed the degenerate cases dl„(z)/dv, v = ± §. The related problem of computing d«/„(z)/óV has been considered by Lee and Radosevich [3], who also present brief numerical tables. References to earlier work may be fo...
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Airy Functions in the Thermodynamic Bethe Ansatz
Thermodynamic Bethe ansatz equations are coupled non-linear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painlevé III and the Toda hierarchy. In the simplest such case the massless limit of these non-linear integral equations can be solved in terms of the Airy f...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1965
ISSN: 0025-5718
DOI: 10.2307/2003972