梅林變換被廣泛用于各種純數(shù)學與應用數(shù)學之中，特別是應用于微分方程和積分方程、狄利克雷級數(shù)的理論中，在數(shù)學物理學、數(shù)論、數(shù)學統(tǒng)計學、漸進展開理論，特別是在特殊函數(shù)和積分變換的理論中都可以找到梅林變換的廣泛應用。本書詳細介紹了梅林變換，共3章，第一章為通式，介紹了包含任意函數(shù)的變換；第二章為初等函數(shù)，介紹了代數(shù)函數(shù)、指數(shù)函數(shù)等；第三章為特殊函數(shù)，介紹了多重對數(shù)函數(shù)、拋物柱面函數(shù)、廣義超幾何函數(shù)等。本書適用于研究人員、工程師、研究生、大學生參考閱讀。
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)
2.1.2. (ax b) and ∣x - a∣
2.1.3. (ax b) (cx d)
2.1.4. (a - x) (bx c) and (x - a) (bx c)
2.1.5. (ax b) (cxv d)
2.1.6. (a-x)-1 (xn bn)r and (x-a)-1 (xn bn)r
2.1.7. (ax2 bx c) (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-bx
2.2.2. ebxm(a-x)n and algebraic functions
2.2.3. e(x) and algebraic functions
2.2.4. (ex±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 ex
2.3.4. Hyperbolic functions and e(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 ((x)) and algebraic functions
2.5.7. In ((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 ((x)), arccos ((x)), and algebraic functions
2.6.2. arcsin ((x)), arecos ((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 ((x)), arccos ((x)), and the logarithmic function
2.6.6. arctan ((x)) and arccot (bx)
2.6.7. arctan ((x)) and the exponential function
2.6.8. arctan ((x)) and trigonometric functions
2.6.9. arctan ((x)) and the logarithmic function
2.6.10. arccsc ((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 ((x)) and elementary functions
2.7.2. arccoshn ((x)) and elementary functions
2.7.3. arctanh (ax) and elementary functions
2.7.4. arccoth (ax) and algebraic functions
2.7.5. arcsechn ((x)) and elementary functions
2.7.6. arccschn((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
編輯手記
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