作者：(俄)Yu.A.布里奇科夫(Yu. A.
页数：16,594页
出版社：哈尔滨工业大学出版社
出版日期：2024
ISBN：9787576712865
电子书格式：pdf/epub/txt
内容简介
梅林变换被广泛用于各种纯数学与应用数学之中，特别是应用于微分方程和积分方程、狄利克雷级数的理论中，在数学物理学、数论、数学统计学、渐进展开理论，特别是在特殊函数和积分变换的理论中都可以找到梅林变换的广泛应用。本书详细介绍了梅林变换，共3章，第一章为通式，介绍了包含任意函数的变换；第二章为初等函数，介绍了代数函数、指数函数等；第三章为特殊函数，介绍了多重对数函数、抛物柱面函数、广义超几何函数等。本书适用于研究人员、工程师、研究生、大学生参考阅读。
目录
Preface
Chapter 1. General Formulas
1.1 Transforms Containing Arbitrary Functions
1.1.1. Basic formulas
1.1.2. f (axr) and the power function
1.1.3. f (axr) and elementary functions
1.1.4. Derivatives of f(x)
1.1.5. Integrals containing f(x)
Chapter 2. Elementary Functions
2.1 Algebraic Functions
2.1.1. (ar – xr) and (xr – ar)α
2.1.2. (ax b)ρ and ∣x – a∣ρ
2.1.3. (ax b)ρ (cx d)σ
2.1.4. (a – x)ρ (bx c)σ and (x – a)ρ (bx c)σ
2.1.5. (axμ b)ρ (cxv d)σ
2.1.6. (a-x)α-1 (xn bn)r and (x-a)α-1 (xn bn)r
2.1.7. (ax2 bx c)ρ (dx e)
2.1.8. Algebraic functions of √ax b
2.1.9. Algebraic functions of √ax2 bx c
2.1.10. Various algebraic functions
2.2 The Exponential Function
2.2.1. e-axr-bxρ
2.2.2. ebxm(a-x)n and algebraic functions
2.2.3. eψ(x) and algebraic functions
2.2.4. (eαx±c)p e-bx
2.3 Hyperbolic Functions
2.3.1. Rational functions of sinh x and cosh x
2.3.2. Hyperbolic and algebraic functions
2.3.3. Hyperbolic functions and eαx
2.3.4. Hyperbolic functions and eψ(x)
2.4 Trigonometric Functions
2.4.1. sin (ax b) and cos(ax b)
2.4.2. Trigonometric and algebraic functions
2.4.3. Trigonometric and the exponential functions
2.4.4. Trigonometric and hyperbolic functions
2.4.5. Products of trigonometric functions
2.4.6. sincn (bx) and elementary functions
2.5 The Logarithmic Function
2.5.1. In (bx) and algebraic functions
2.5.2. In (bx c) and algebraic functions
2.5.3. In(ax b)/(cx d)，In∣(ax b)/(cx d)∣and algebraic functions
2.5.4. In(ax2 bx c) and algebraic functions
2.5.5. In(ax2 bx c)/(dx2 ex f)and algebraic functions
2.5.6. In (ψ(x)) and algebraic functions
2.5.7. In (ψ(x)) and the exponential function
2.5.8. The logarithmic and hyperbolic or trigonometric functions
2.5.9. Products of logarithms
2.6 Inverse Trigonometric Functions
2.6.1. arcsin (ψ(x)), arccos (ψ(x)), and algebraic functions
2.6.2. arcsin (ψ(x)), arecos (ψ(x)), and the exponential function
2.6.3. arccos (bx) and hyperbolic or trigonometric functions
2.6.4. Trigonometric functions of inverse trigonometric functions
2.6.5. arcsin (ψ(x)), arccos (ψ(x)), and the logarithmic function
2.6.6. arctan (ψ(x)) and arccot (bx)
2.6.7. arctan (ψ(x)) and the exponential function
2.6.8. arctan (ψ(x)) and trigonometric functions
2.6.9. arctan (ψ(x)) and the logarithmic function
2.6.10. arccsc (ψ(x)) and algebraic functions
2.6.11. arcsec (bx) and algebraic functions
2.6.12. Products of inverse trigonometric functions
2.7 Inverse Hyperbolic Functions
2.7.1. arcsinhn (ψ(x)) and elementary functions
2.7.2. arccoshn (ψ(x)) and elementary functions
2.7.3. arctanh (ax) and elementary functions
2.7.4. arccoth (ax) and algebraic functions
2.7.5. arcsechn (ψ(x)) and elementary functions
2.7.6. arccschn(ψ(x)) and elementary functions
2.7.7. Hypebolic functions of inverse hyperbolic functions
Chapter 3. Special Functions
Appendix Ⅰ. Some Properties of the Mellin Transforms
Appendix Ⅱ. Conditions of Convergence
Bibliography
Index of Notations for Functions and Constants
Index of Notations for Symbols
编辑手记
Chapter 1. General Formulas
1.1 Transforms Containing Arbitrary Functions
1.1.1. Basic formulas
1.1.2. f (axr) and the power function
1.1.3. f (axr) and elementary functions
1.1.4. Derivatives of f(x)
1.1.5. Integrals containing f(x)
Chapter 2. Elementary Functions
2.1 Algebraic Functions
2.1.1. (ar – xr) and (xr – ar)α
2.1.2. (ax b)ρ and ∣x – a∣ρ
2.1.3. (ax b)ρ (cx d)σ
2.1.4. (a – x)ρ (bx c)σ and (x – a)ρ (bx c)σ
2.1.5. (axμ b)ρ (cxv d)σ
2.1.6. (a-x)α-1 (xn bn)r and (x-a)α-1 (xn bn)r
2.1.7. (ax2 bx c)ρ (dx e)
2.1.8. Algebraic functions of √ax b
2.1.9. Algebraic functions of √ax2 bx c
2.1.10. Various algebraic functions
2.2 The Exponential Function
2.2.1. e-axr-bxρ
2.2.2. ebxm(a-x)n and algebraic functions
2.2.3. eψ(x) and algebraic functions
2.2.4. (eαx±c)p e-bx
2.3 Hyperbolic Functions
2.3.1. Rational functions of sinh x and cosh x
2.3.2. Hyperbolic and algebraic functions
2.3.3. Hyperbolic functions and eαx
2.3.4. Hyperbolic functions and eψ(x)
2.4 Trigonometric Functions
2.4.1. sin (ax b) and cos(ax b)
2.4.2. Trigonometric and algebraic functions
2.4.3. Trigonometric and the exponential functions
2.4.4. Trigonometric and hyperbolic functions
2.4.5. Products of trigonometric functions
2.4.6. sincn (bx) and elementary functions
2.5 The Logarithmic Function
2.5.1. In (bx) and algebraic functions
2.5.2. In (bx c) and algebraic functions
2.5.3. In(ax b)/(cx d)，In∣(ax b)/(cx d)∣and algebraic functions
2.5.4. In(ax2 bx c) and algebraic functions
2.5.5. In(ax2 bx c)/(dx2 ex f)and algebraic functions
2.5.6. In (ψ(x)) and algebraic functions
2.5.7. In (ψ(x)) and the exponential function
2.5.8. The logarithmic and hyperbolic or trigonometric functions
2.5.9. Products of logarithms
2.6 Inverse Trigonometric Functions
2.6.1. arcsin (ψ(x)), arccos (ψ(x)), and algebraic functions
2.6.2. arcsin (ψ(x)), arecos (ψ(x)), and the exponential function
2.6.3. arccos (bx) and hyperbolic or trigonometric functions
2.6.4. Trigonometric functions of inverse trigonometric functions
2.6.5. arcsin (ψ(x)), arccos (ψ(x)), and the logarithmic function
2.6.6. arctan (ψ(x)) and arccot (bx)
2.6.7. arctan (ψ(x)) and the exponential function
2.6.8. arctan (ψ(x)) and trigonometric functions
2.6.9. arctan (ψ(x)) and the logarithmic function
2.6.10. arccsc (ψ(x)) and algebraic functions
2.6.11. arcsec (bx) and algebraic functions
2.6.12. Products of inverse trigonometric functions
2.7 Inverse Hyperbolic Functions
2.7.1. arcsinhn (ψ(x)) and elementary functions
2.7.2. arccoshn (ψ(x)) and elementary functions
2.7.3. arctanh (ax) and elementary functions
2.7.4. arccoth (ax) and algebraic functions
2.7.5. arcsechn (ψ(x)) and elementary functions
2.7.6. arccschn(ψ(x)) and elementary functions
2.7.7. Hypebolic functions of inverse hyperbolic functions
Chapter 3. Special Functions
Appendix Ⅰ. Some Properties of the Mellin Transforms
Appendix Ⅱ. Conditions of Convergence
Bibliography
Index of Notations for Functions and Constants
Index of Notations for Symbols
编辑手记
