♦ 6 matching pages ♦
6 matching pages
… ►Assume that is piecewise continuous on and of exponential growth, that is, constants and exist such that …
§8.24 Physical Applications… ►The function appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). ►
§8.24(iii) Generalized Exponential Integral►The function , with , appears in theories of transport and radiative equilibrium (Hopf (1934), Kourganoff (1952), Altaç (1996)). ►With more general values of , supplies fundamental auxiliary functions that are used in the computation of molecular electronic integrals in quantum chemistry (Harris (2002), Shavitt (1963)), and also wave acoustics of overlapping sound beams (Ding (2000)).
… ►However, since the growth near the singularities of the differential equation is algebraic rather than exponential, the resulting instabilities in the numerical integration might be tolerable in some cases. …
13.19.1 .… ►
13.19.2 ,… ►
13.19.3 .… ►For an asymptotic expansion of as that is valid in the sector and where the real parameters , are subject to the growth conditions , , see Wong (1973a). …
28.29.7►iff is an eigenvalue of the matrix … ►
28.29.10… ►A nontrivial solution is either a Floquet solution with respect to , or is a Floquet solution with respect to . … ►Its order of growth for is exactly ; see Magnus and Winkler (1966, Chapter II, pp. 19–28). …
Calculation of Special Functions: The Gamma Function, the Exponential Integrals and Error-Like Functions.
CWI Tract, Vol. 10, Stichting Mathematisch Centrum, Centrum voor Wiskunde en
Integrating products of Bessel functions with an additional exponential or rational factor.
Comput. Phys. Comm. 178 (8), pp. 578–590.
Rational approximations for exponential integrals
Acad. Roy. Belg. Bull. Cl. Sci. (5) 56, pp. 1064–1072.
On the growth of convergence radii for the eigenvalues of the Mathieu equation.
Math. Nachr. 192, pp. 239–253.