Quantum Calculus
Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitabi...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2002, 2002
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| Edition: | 1st ed. 2002 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 q-Derivative and h-Derivative
- 2 Generalized Taylor’s Formula for Polynomials
- 3 q-Analogue of (x &t- 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 Bino-mial 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-Trigonometrie 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 and of Four Triangul?r Numbers
- 18 q-Antiderivative
- 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 Symmetrie Quantum Calculus
- Literature