Uniform Asymptotic Expansions of Confluent Hypergeometric Functions and Whittaker Functions |
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Contents
Introduction | 1 |
Notations | 7 |
Theorems of Olver and extensions | 16 |
Copyright | |
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A₁ Airy functions analytic continuation arbitrary constants argz asymptotic direction asymptotic forms asymptotisk udvikling asymptotiske udviklinger Bessel functions bounded branch-points chapter coefficients confluent hypergeometric functions corresponding deduced defined denote differential equation Erdélyi error terms expansions of confluent follows formulas functions and Whittaker h₁(m Hence henholdsvis indents independent infinity integral interval Jordan arcs Laguerre polynomials level curves Liouville mapping method nærværende notations O-terms Olver's theorem områder overgangspunkt parameter positive constant positive number principal curves proof real axis real x-axis regions of validity Riemann surface satisfied Schwarzian derivative section 2.1 shadow zones sheets simply-connected simply-connected domain Skovgaard Slater 29 solutions straight line segment subregion theorems of Olver tilfælde transformation transition points ubegrænsede um+1 unbounded regions UNIFORM ASYMPTOTIC EXPANSIONS uniformly with respect variable W₂ Whittaker functions x-sheets z-maps z-plane z→aj zero