Asymptotic expansions

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Asymptotic expansions / A. Erdélyi

資料種別:: 図書
出版情報:: New York : Dover Publications, 1956
形態:: vi, 108 p. ; 21 cm
シリーズ名:: Dover books on advanced mathematics <BA00209096>
著者名:: Erdélyi, Arthur <DA00354411>
ISBN:: 9780486603186 [0486603180]
書誌ID:: BA0019998X

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Asymptotic expansions
A. Erdélyi , Dover Publications , 1956

書誌詳細

注記:

"An unabridged and unaltered republication of Technical report 3, prepared under contract Nonr-220 (11) for the Office of Naval Research reference No. NR 043-121."
Includes bibliographies

主題:

Asymptotic expansions

言語:

英語

目次情報:

Introduction

References

Asymptotic Series / Chapter I：

O-symbols / 1.1：

Asymptotic sequences / 1.2：

Asymptotic expansions / 1.3：

Linear operations with asymptotic expansions / 1.4：

Other operations with asymptotic expansions / 1.5：

Asymptotic power series / 1.6：

Summation of asymptotic series / 1.7：

Integrals / Chapter II：

Integration by parts / 2.1：

Laplace integrals / 2.2：

Critical points / 2.3：

Laplace's method / 2.4：

The method of steepest descents / 2.5：

Airy's integral / 2.6：

Further examples / 2.7：

Fourier integrals / 2.8：

The method of stationary phase / 2.9：

Singularities of Differential Equations / Chapter III：

Classification of singularities / 3.1：

Normal solutions / 3.2：

The integral equation and its solution / 3.3：

Asymptotic expansions of the solutions / 3.4：

Complex variable / 3.5：

Stokes' phenomenon

Bessel functions of order zero / 3.6：

Differential Equations with a Large Parameter / Chapter IV：

Liouville's problem / 4.1：

Formal solutions / 4.2：

Asymptotic solutions / 4.3：

Application to Bessel functions / 4.4：

Transition points / 4.5：

Airy functions / 4.6：

Asymptotic solutions valid in the transition region / 4.7：

Uniform asymptotic representations of Bessel functions / 4.8：

Introduction

References

Asymptotic Series / Chapter I：

O-symbols / 1.1：

Asymptotic sequences / 1.2：

Asymptotic expansions / 1.3：

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