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Hyperterminants. II. (English) Zbl 0910.34014
This paper is in continuation of computation to arbitrary precision of hyperterminants that occur in hyperasymptotic expansions for solutions to second-order linear differential equations and integrals with two saddles [the author, part I, J. Comput. Appl. Math. 76, No. 1-2, 255-264 (1996; Zbl 0866.65011)]. The author concerns the computation of the hyperterminants that occur in hyperasymptotic expansions of higher-order linear differential equations, nonlinear differential equations and integrals with more than two saddles. The author gives new integral representations for the hyperterminants. With these integral representations, the author is able to obtain convergent and computable series expansions for hyperterminants. Another feature of the results is the occurence of hypergeometric functions.
Reviewer: R.S.Dahiya (Ames)

MSC:
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
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References:
[1] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions with formulas, graphs, and mathematical tables, () · Zbl 0515.33001
[2] Berry, M.V.; Howls, C.J., Hyperasymptotics for integrals with saddles, (), 657-675 · Zbl 0764.30031
[3] Howls, C.J., Hyperasymptotics for integrals with finite endpoints, (), 373-396 · Zbl 0773.30040
[4] Howls, C.J., Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem, (), 2271-2294 · Zbl 1067.58501
[5] Olde Daalhuis, A.B., Hyperterminants I, J. comput. appl. math., 76, 255-264, (1996) · Zbl 0866.65011
[6] Olde Daalhuis, A.B., Hyperasymptotic solutions of higher order differential equations with a singularity of rank one, (), 1-29 · Zbl 0919.34012
[7] Temme, N.M., Special functions: an introduction to the classical functions of mathematical physics, (1996), Wiley New York · Zbl 0863.33002
[8] Titchmarsh, E.C., The theory of functions, (1939), Oxford Univ. Press London · Zbl 0022.14602
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