Quantum Calculus Book

	Introduction
1	q-Derivative and h-Derivative	1
2	Generalized Taylor's Formula for Polynomials	5
3	q-Analogue of (x - a)[superscript n], n an Integer, and q-Derivatives of Binomials	7
4	q-Taylor's Formula for Polynomials	12
5	Gauss's Binomial Formula and a Noncommutative Binomial Formula	14
6	Properties of q-Binomial Coefficients	17
7	q-Binomial Coefficients and Linear Algebra over Finite Fields	21
8	q-Taylor's Formula for Formal Power Series and Heine's Binomial Formula	27
9	Two Euler's Identities and Two q-Exponential Functions	29
10	q-Trigonometric Functions	33
11	Jacobi's Triple Product Identity	35
12	Classical Partition Function and Euler's Product Formula	37
13	q-Hypergeometric Functions and Heine's Formula	43
14	More on Heine's Formula and the General Binomial	47
15	Ramanujan Product Formula	50
16	Explicit Formulas for Sums of Two and of Four Squares	56
17	Explicit Formulas for Sums of Two and of Four Triangular Numbers	60
18	q-Antiderivative	64
19	Jackson Integral	67
20	Fundamental Theorem of q-Calculus and Integration by Parts	73
21	q-Gamma and q-Beta Functions	76
22	h-Derivative and h-Integral	80
23	Bernoulli Polynomials and Bernoulli Numbers	85
24	Sums of Powers	90
25	Euler-Maclaurin Formula	92
26	Symmetric Quantum Calculus	99
	App.: A List of q-Antiderivatives	106
	Literature	109
	Index	111