A. Erdélyi
Asymptotic Expansions
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Asymptotic Expansions
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Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.
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Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.
Produktdetails
- Produktdetails
- Verlag: Dover Publications
- Seitenzahl: 128
- Erscheinungstermin: 18. November 2010
- Englisch
- Abmessung: 203mm x 138mm x 9mm
- Gewicht: 168g
- ISBN-13: 9780486603186
- ISBN-10: 0486603180
- Artikelnr.: 24333338
- Verlag: Dover Publications
- Seitenzahl: 128
- Erscheinungstermin: 18. November 2010
- Englisch
- Abmessung: 203mm x 138mm x 9mm
- Gewicht: 168g
- ISBN-13: 9780486603186
- ISBN-10: 0486603180
- Artikelnr.: 24333338
Introduction; References Chapter I. Asymptotic Series 1.1 O-symbols 1.2
Asymptotic sequences 1.3 Asymptotic expansions 1.4 Linear operations with
asymptotic expansions 1.5 Other operations with asymptotic expansions 1.6
Asymptotic power series 1.7 Summation of asymptotic series References
Chapter II. Integrals 2.1 Integration by parts 2.2 Laplace integrals 2.3
Critical points 2.4 Laplace's method 2.5 The method of steepest descents
2.6 Airy's integral 2.7 Further examples 2.8 Fourier integrals 2.9 The
method of stationary phase References Chapter III. Singularities of
Differential Equations 3.1 Classification of singularities 3.2 Normal
solutions 3.3 The integral equation and its solution 3.4 Asymptotic
expansions of the solutions 3.5 Complex variable. Stokes' phenomenon 3.6
Bessel functions of order zero References Chapter IV. Differential
Equations with a Large Parameter 4.1 Liouville's problem 4.2 Formal
solutions 4.3 Asymptotic solutions 4.4 Application to Bessel functions 4.5
Transition points 4.6 Airy functions 4.7 Asymptotic solutions valid in the
transition region 4.8 Uniform asymptotic representations of Bessel
functions References
Asymptotic sequences 1.3 Asymptotic expansions 1.4 Linear operations with
asymptotic expansions 1.5 Other operations with asymptotic expansions 1.6
Asymptotic power series 1.7 Summation of asymptotic series References
Chapter II. Integrals 2.1 Integration by parts 2.2 Laplace integrals 2.3
Critical points 2.4 Laplace's method 2.5 The method of steepest descents
2.6 Airy's integral 2.7 Further examples 2.8 Fourier integrals 2.9 The
method of stationary phase References Chapter III. Singularities of
Differential Equations 3.1 Classification of singularities 3.2 Normal
solutions 3.3 The integral equation and its solution 3.4 Asymptotic
expansions of the solutions 3.5 Complex variable. Stokes' phenomenon 3.6
Bessel functions of order zero References Chapter IV. Differential
Equations with a Large Parameter 4.1 Liouville's problem 4.2 Formal
solutions 4.3 Asymptotic solutions 4.4 Application to Bessel functions 4.5
Transition points 4.6 Airy functions 4.7 Asymptotic solutions valid in the
transition region 4.8 Uniform asymptotic representations of Bessel
functions References
Introduction; References Chapter I. Asymptotic Series 1.1 O-symbols 1.2
Asymptotic sequences 1.3 Asymptotic expansions 1.4 Linear operations with
asymptotic expansions 1.5 Other operations with asymptotic expansions 1.6
Asymptotic power series 1.7 Summation of asymptotic series References
Chapter II. Integrals 2.1 Integration by parts 2.2 Laplace integrals 2.3
Critical points 2.4 Laplace's method 2.5 The method of steepest descents
2.6 Airy's integral 2.7 Further examples 2.8 Fourier integrals 2.9 The
method of stationary phase References Chapter III. Singularities of
Differential Equations 3.1 Classification of singularities 3.2 Normal
solutions 3.3 The integral equation and its solution 3.4 Asymptotic
expansions of the solutions 3.5 Complex variable. Stokes' phenomenon 3.6
Bessel functions of order zero References Chapter IV. Differential
Equations with a Large Parameter 4.1 Liouville's problem 4.2 Formal
solutions 4.3 Asymptotic solutions 4.4 Application to Bessel functions 4.5
Transition points 4.6 Airy functions 4.7 Asymptotic solutions valid in the
transition region 4.8 Uniform asymptotic representations of Bessel
functions References
Asymptotic sequences 1.3 Asymptotic expansions 1.4 Linear operations with
asymptotic expansions 1.5 Other operations with asymptotic expansions 1.6
Asymptotic power series 1.7 Summation of asymptotic series References
Chapter II. Integrals 2.1 Integration by parts 2.2 Laplace integrals 2.3
Critical points 2.4 Laplace's method 2.5 The method of steepest descents
2.6 Airy's integral 2.7 Further examples 2.8 Fourier integrals 2.9 The
method of stationary phase References Chapter III. Singularities of
Differential Equations 3.1 Classification of singularities 3.2 Normal
solutions 3.3 The integral equation and its solution 3.4 Asymptotic
expansions of the solutions 3.5 Complex variable. Stokes' phenomenon 3.6
Bessel functions of order zero References Chapter IV. Differential
Equations with a Large Parameter 4.1 Liouville's problem 4.2 Formal
solutions 4.3 Asymptotic solutions 4.4 Application to Bessel functions 4.5
Transition points 4.6 Airy functions 4.7 Asymptotic solutions valid in the
transition region 4.8 Uniform asymptotic representations of Bessel
functions References