Difference between revisions of "Book:Victor Kac/Quantum Calculus"
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===Contents=== | ===Contents=== | ||
| + | :Introduction | ||
| + | :1 $q$-Derivative and $h$-Derivative | ||
| + | ::---------- | ||
| + | ::[[Q-derivative|$(1.5)$]] | ||
| + | ::---------- | ||
| + | ::[[Q-number|$(1.9)$]] | ||
| + | :2 Generalized Taylor's Formula for Polynomials | ||
| + | :3 $q$-Analogue of $(x-a)^n$, $n$ an Integer, and $q$-Derivatives of Binomials | ||
| + | ::[[Q-factorial|$(3.1)$]] | ||
| + | ::---------- | ||
| + | ::[[Q-number|$(3.8)$]] | ||
| + | :4 $q$-Taylor's Formula for Polynomials | ||
| + | :5 Gauss's Binomial Formula and a Noncommutative Binomial Formula | ||
| + | :6 Properties of $q$-Binomial Coefficients | ||
| + | :7 $q$-Binomial Coefficients and Linear Algebra over Finite Fields | ||
| + | :8 $q$-Taylor's Formula for Formal Power Series and Heine's Binomial Formula | ||
| + | :9 Two Euler's Identities and two $q$-Exponential Functions | ||
| + | ::---------- | ||
| + | ::[[Q-exponential E sub q|$(9.5)$]] | ||
| + | ::---------- | ||
| + | ::[[Q-exponential E sub 1/q|$(9.10)$]] | ||
| + | :10 $q$-Trigonometric functions | ||
| + | :11 Jacobi's Triple Product Identity | ||
| + | :12 Classical Partition Function and Euler's Product Formula | ||
| + | :13 $q$-Hypergeometric Functions and Heine's Formula | ||
| + | :14 More on Heine's Formula and the General Binomial | ||
| + | :15 Ramanujan Product Formula | ||
| + | :16 Explicit Formulas for Sums of Two and of Four Squares | ||
| + | :17 Explicit Formulas for Sums of Two of Four Triangular Numbers | ||
| + | :18 $q$-Antiderivatives | ||
| + | :19 Jackson Integral | ||
| + | :20 Fundamental Theorem of $q$-Calculus and Integration by Parts | ||
| + | :21 $q$-Gamma and $q$-Beta Functions | ||
| + | :22 $h$-Derivative and $h$-Integral | ||
| + | :23 Bernoulli Polynomials and Bernoulli Numbers | ||
| + | :24 Sums of Powers | ||
| + | :25 Euler-Maclaurin Formula | ||
| + | :26 Symmetric Quantum Calculus | ||
| + | :Appendix: A List of $q$-Antiderivatives | ||
| + | :Literature | ||
| + | :Index | ||
[[Category:Book]] | [[Category:Book]] | ||
Latest revision as of 05:16, 21 January 2017
Victor Kac and Pokman Cheung: Quantum Calculus
Published $2002$, Springer.
Contents
- Introduction
- 1 $q$-Derivative and $h$-Derivative
- 2 Generalized Taylor's Formula for Polynomials
- 3 $q$-Analogue of $(x-a)^n$, $n$ an Integer, and $q$-Derivatives of Binomials
- 4 $q$-Taylor's Formula for Polynomials
- 5 Gauss's Binomial Formula and a Noncommutative Binomial Formula
- 6 Properties of $q$-Binomial Coefficients
- 7 $q$-Binomial Coefficients and Linear Algebra over Finite Fields
- 8 $q$-Taylor's Formula for Formal Power Series and Heine's Binomial Formula
- 9 Two Euler's Identities and two $q$-Exponential Functions
- 10 $q$-Trigonometric functions
- 11 Jacobi's Triple Product Identity
- 12 Classical Partition Function and Euler's Product Formula
- 13 $q$-Hypergeometric Functions and Heine's Formula
- 14 More on Heine's Formula and the General Binomial
- 15 Ramanujan Product Formula
- 16 Explicit Formulas for Sums of Two and of Four Squares
- 17 Explicit Formulas for Sums of Two of Four Triangular Numbers
- 18 $q$-Antiderivatives
- 19 Jackson Integral
- 20 Fundamental Theorem of $q$-Calculus and Integration by Parts
- 21 $q$-Gamma and $q$-Beta Functions
- 22 $h$-Derivative and $h$-Integral
- 23 Bernoulli Polynomials and Bernoulli Numbers
- 24 Sums of Powers
- 25 Euler-Maclaurin Formula
- 26 Symmetric Quantum Calculus
- Appendix: A List of $q$-Antiderivatives
- Literature
- Index
