图书信息
图书目录
Fourier级数和正交多项式（Fourier Series and Orthogonal Polynomials）（影印版）
暂无简介
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：
250.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次印刷时间：
2026年
- 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
- 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
- 1. Boundary value problem in a cube
- 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
- 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
- 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
- 5. Generating function
- 6. Wave equation of the linear oscillator
- X. LAGUERRE POLYNOMIALS
- 1. Derivative definition
- 2. Orthogonality; normalizing factor
- 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
- 3. Convergence
- 4. Magnitude of the coefficients
- 5. Convergence
- 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
