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Fourier级数和正交多项式（Fourier Series and Orthogonal Polynomials）（影印版）

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作者：

Dunham Jackson

定价：

135.00 元

出版时间：

2026-03-27

ISBN：

978-7-04-065927-6

物料号：

65927-00

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

重点项目：

暂无

版面字数：

250千字

开本：

16开

装帧形式：

精装

页数：

暂无

最新
印次时间：

2026年01月

目录
- 前辅文
- I. FOURIER SERIES
  - 1. Definition of Fourier series
  - 2. Orthogonality of sines and cosines
  - 3. Determination of the coefficients
  - 4. Series of cosines and series of sines
  - 5. Examples
  - 6. Magnitude of coefficients under special hypotheses
  - 7. Riemann's theorem on limit of general coefficient
  - 8. Evaluation of a sum of cosines
  - 9. Integral formula for partial sum of Fourier series
  - 10. Convergence at a point of continuity
  - 11. Uniform convergence under special hypotheses
  - 12. Convergence at a point of discontinuity
  - 13. Sufficiency of conditions relating to a restricted neighborhood
  - 14. Weierstrass's theorem on trigonometric approximation
  - 15. Least-square property
  - 16. Parseval's theorem
  - 17. Summation of series
  - 18. Fejér's theorem for a continuous function
  - 19. Proof of Weierstrass's theorem by means of de la Vallée Poussin's integral
  - 20. The Lebesgue constants
  - 21. Proof of uniform convergence by the method of Lebesgue
- II. LEGENDRE POLYNOMIALS
  - 1. Preliminary orientation
  - 2. Definition of the Legendre polynomials by means of the generating function
  - 3. Recurrence formula
  - 4. Differential equation and related formulas
  - 5. Orthogonality
  - 6. Normalizing factor
  - 7. Expansion of an arbitrary function in series
  - 8. Christoffel's identity
  - 9. Solution of the differential equation
  - 10. Rodrigues's formula
  - 11. Integral representation
  - 12. Bounds of Pn(x)
  - 13. Convergence at a point of continuity interior to the interval
  - 14. Convergence at a point of discontinuity interior to the interval
- III. BESSEL FUNCTIONS
  - 1. Preliminary orientation
  - 2. Definition of J0(x)
  - 3. Orthogonality
  - 4. Integral representation of J0(x)
  - 5. Zeros of J0(x) and related functions
  - 6. Expansion of an arbitrary function in series
  - 7. Definition of Jn(x)
  - 8. Orthogonality: developments in series
  - 9. Integral representation of Jn(x)
  - 10. Recurrence formulas
  - 11. Zeros
  - 12. Asymptotic formula
  - 13. Orthogonal functions arising from linear boundary value problems
- IV. BOUNDARY VALUE PROBLEMS
  - 1. Fourier series: Laplace's equation in an infinite strip
  - 2. Fourier series: Laplace's equation in a rectangle
  - 3. Fourier series: vibrating string
  - 4. Fourier series: damped vibrating string
  - 5. Polar coordinates in the plane
  - 6. Fourier series: Laplace's equation in a circle; Poisson's integral
  - 7. Transformation of Laplace's equation in three dimensions
  - 8. Legendre series: Laplace's equation in a sphere
  - 9. Bessel series: Laplace's equation in a cylinder
  - 10. Bessel series: circular drumhead
- V. DOUBLE SERIES; LAPLACE SERIES
  - 1. Boundary value problem in a cube; double Fourier series
  - 2. General spherical harmonics
  - 3. Laplace series
  - 4. Harmonic polynomials
  - 5. Rotation of axes
  - 6. Integral representation for group of terms in the Laplace series
  - 7. Completeness of the Laplace series
  - 8. Boundary value problem in a cylinder; series involving Bessel functions of positive order
- VI. THE PEARSON FREQUENCY FUNCTIONS
  - 1. The Pearson differential equation
  - 2. Quadratic denominator, real roots
  - 3. Quadratic denominator, complex roots
  - 4. Linear or constant denominator
  - 5. Finiteness of moments
- VII. ORTHOGONAL POLYNOMIALS
  - 1. Weight function
  - 2. Schmidt's process
  - 3. Orthogonal polynomials corresponding to an arbitrary weight function
  - 4. Development of an arbitrary function in series
  - 5. Formula of recurrence
  - 6. Christoffel-Darboux identity
  - 7. Symmetry
  - 8. Zeros
  - 9. Least-square property
  - 10. Differential equation
- VIII. JACOBI POLYNOMIALS
  - 1. Derivative definition
  - 2. Orthogonality
  - 3. Leading coefficients
  - 4. Normalizing factor; series of Jacobi polynomials
  - 5. Recurrence formula
  - 6. Differential equation
- IX. HERMITE POLYNOMIALS
  - 1. Derivative definition
  - 2. Orthogonality and normalizing factor
  - 3. Hermite and Gram-Charlier series
  - 4. Recurrence formulas; differential equation
  - 5. Generating function
  - 6. Wave equation of the linear oscillator
- X. LAGUERRE POLYNOMIALS
  - 1. Derivative definition
  - 2. Orthogonality; normalizing factor; Laguerre series
  - 3. Differential equation and recurrence formulas
  - 4. Generating function
  - 5. Wave equation of the hydrogen atom
- XI. CONVERGENCE
  - 1. Scope of the discussion
  - 2. Magnitude of the coefficients; first hypothesis
  - 3. Convergence; first hypothesis
  - 4. Magnitude of the coefficients; second hypothesis
  - 5. Convergence; second hypothesis
  - 6. Special Jacobi polynomials
  - 7. Multiplication or division of the weight function by a polynomial
  - 8. Korous's theorem on bounds of orthonormal polynomials
- EXERCISES
- BIBLIOGRAPHY
- INDEX

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Fourier级数和正交多项式（Fourier Series and Orthogonal Polynomials）（影印版）

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