Approximation Methods in Transcendental Function Computations and Some Physical Applications

D. V. Chudnovsky and G. V. Chudnovsky
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D. V. Chudnovsky: Columbia University
G. V. Chudnovsky: Columbia University

Chapter 4 in Number Theory: New York Seminar 1991–1995, 1996, pp 43-69 from Springer

Abstract: Abstract High precision solution of extremal and complex analytic approximations problems that can be represented in terms of multiple integrals or integral equations involving hypergeometric functions are examined. Fast algorithms of computations of (approximate) solutions are presented that are well suited for parallelization. Among problems considered are: WKB and adelic asymptotics of multidimensional hypergeometric Padé approximations to classical functions, and high accuracy computations of high order eigenvalues and eigenstates for 2D and 3D domains of complex geometry. Methods based on boundary integrals, Galerkin techniques for various eigenfunction expansions and singularity analysis are examined.

Keywords: Spectral Problem; Linear Differential Equation; Hyperbolic Manifold; Asymptotic Series; Diophantine Approximation (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2418-1_4

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DOI: 10.1007/978-1-4612-2418-1_4

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