梅林变换手册:英文

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