Difference between revisions of "Book:Leonard Lewin/Polylogarithms and Associated Functions/Second Edition"
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:CHAPTER 1. THE DILOGARITHM | :CHAPTER 1. THE DILOGARITHM | ||
::1.1. Introduction and Elementary Considerations | ::1.1. Introduction and Elementary Considerations | ||
| + | :::[[Dilogarithm|$(1.1)$]] | ||
| + | :::[[Taylor series of log(1-z)|$(1.2)$]] | ||
| + | :::[[Relationship between dilogarithm and log(1-z)/z|$(1.3)$]] | ||
| + | :::--------- | ||
| + | :::[[Derivative of Li 2(-1/x)|$(1.6)$]] | ||
| + | :::[[Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)|$(1.7)$]] | ||
| + | :::[[Relationship between Li 2(1),Li 2(-1), and pi|$(1.8)$]] | ||
| + | :::[[Li 2(1)=pi^2/6|$(1.9)$]] | ||
::1.2. Extensions to Large Real Values of $z$ | ::1.2. Extensions to Large Real Values of $z$ | ||
::1.3. Functional Equations Involving a Single Variable | ::1.3. Functional Equations Involving a Single Variable | ||
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:Suggestions for Further Study | :Suggestions for Further Study | ||
:Index | :Index | ||
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Latest revision as of 05:15, 21 January 2017
Leonard Lewin: Polylogarithms and Associated Functions (2nd Edition)
Published $1981$, North-Holland Publishing Co., New York-Amsterdam.
BiBTeX
@book {MR618278,
AUTHOR = {Lewin, Leonard},
TITLE = {Polylogarithms and associated functions},
NOTE = {With a foreword by A. J. Van der Poorten},
PUBLISHER = {North-Holland Publishing Co., New York-Amsterdam},
YEAR = {1981},
PAGES = {xvii+359},
ISBN = {0-444-00550-1},
MRCLASS = {33A70 (10H99)},
MRNUMBER = {618278},
}
Contents
- Foreward
- Preface
- Preface to the Previous Work
- CHAPTER 1. THE DILOGARITHM
- 1.1. Introduction and Elementary Considerations
- 1.2. Extensions to Large Real Values of $z$
- 1.3. Functional Equations Involving a Single Variable
- 1.4. Numerical Relations
- 1.5. Functional Relations Involving Two Variables
- 1.6. Newman's Functional Equation
- 1.7. Functional Equations Involving Several Variables
- 1.8. Legendre's Chi-functions
- 1.9. Some Miscellaneous Results
- 1.10. A Survey of Definitions and Notations
- 1.11. Relations to Other Mathematical Functions
- 1.12. Occurrence in Physical Problems
- CHAPTER 2. THE INVERSE TANGENT INTEGRAL
- 2.1. Elementary Considerations and Definition
- 2.2. The Inversion Relations
- 2.3. The Duplication Formula
- 2.4. Some Numerical Relations
- 2.5. The Triplication Formula
- 2.6. The Multiplication Formula for Odd Multiples
- 2.7. The Quadruplication Formula
- 2.8. Functional Equations Involving Several Variables
- CHAPTER 3. THE GENERALIZED INVERSE TANGENT INTEGRAL
- 3.1. Introduction and Elementary Properties
- 3.3. Differentiation with Respect to the Parameter
- 3.4. Formulas Arising from a Change of Variable
- 3.5. Formulas Arising form Inverse Tangent Integrals of Bilinear Argument
- 3.6. Factorization Theorems
- 3.7. Multiplication Theorems
- 3.8. Derived Relations
- 3.9. Special Values of the Parameter
- 3.10. An Addition Equation Involving Argument and Parameter
- CHAPTER 4. CLAUSEN'S INTEGRAL
- 4.1 Definition and Elementary Properties
- 4.2 Periodic Properties
- 4.3 The Factorization Theorem
- 4.4 Series Expansions
- 4.5 Integral Relations
- 4.6 Functional Equations
- 4.7 Geometrical Connections
- CHAPTER 5. THE DILOGARITHM OF COMPLEX ARGUMENT
- 5.1 Resolution into Real and Imaginary Parts
- 5.2 The Factorization Theorem
- 5.3 Special Values of the Argument
- 5.4 Functional Equations Involving a Single Variable
- 5.5 Reduction of $\mathrm{Li}_2(x,\theta)$ for Special Values of $\theta$
- 5.6 Newman's Functional Equation Involving Two Variables
- 5.7 Derived Functional Equations
- 5.8 Consequences of the Duplication Formula
- 5.9 An Addition Formula for the Angular Parameter
- CHAPTER 6. THE TRILOGARITHM
- 6.1 Introduction and Elementary Considerations
- 6.2 Functional Equations of a Single Variable
- 6.3 Numerical Relations
- 6.4 A Consideration of Some Complex Forms
- 6.5 Functional Equations of Two Variables
- 6.6 A Further Consideration of Complex Forms
- 6.7 Functional Equations of Two Variables
- 6.8 A Functional Equation of Newman's Type
- 6.9 Functional Equations Involving Several Variables
- CHAPTER 7. THE HIGHER-ORDER FUNCTIONS
- 7.1 Introduction and Definitions
- 7.2 The Inversion Equation and Its Consequences
- 7.3 The Factorization Theorem
- 7.4 Associated Integrals
- 7.5 The Associated Clausen Functions
- 7.6 Integral Relations for the Fourth-Order Polylogarithm
- 7.7 Functional Equations for the Fourth-Order Polylogarithm
- 7.8 Functional Equations for the Fifth-Order Polylogarithm
- 7.9 The Log-Sine Integrals
- 7.10 Results from a Contour Integration
- 7.11 Golden-Cut and Related Integrals
- 7.12 Polylogarithms of Nonintegral Order
- 7.13 Higher-Order Polylogarithms
- CHAPTER 8. INTEGRATION OF FUNCTIONS AND SUMMATION OF SERIES
- 8.1 Reduction of a Class of Algebraic and Logarithmic Expressions
- 8.2 Reduction of Trigonometric Forms
- 8.3 Summation of Series
- 8.4 Integrals from the Higher-Order Functions
- 8.5 Definite Trigonometric Integrals
- APPENDIX. REFERENCE DATA AND TABLES
- A.1. Glossary of Notation
- A.2. List of Selected Formulas
- A.3. Reference List of Integrals
- A.4. Tabulated Values
- Bibliography
- Suggestions for Further Study
- Index
