Author | Kac, Victor. author |
---|---|
Title | Quantum Calculus [electronic resource] / by Victor Kac, Pokman Cheung |
Imprint | New York, NY : Springer New York, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0071-7 |
Descript | IX, 112 p. online resource |
1 q-Derivative and h-Derivative -- 2 Generalized Taylorโs Formula for Polynomials -- 3 q-Analogue of (x &t- a)n, n an Integer, and q-Derivatives of Binomials -- 4 q-Taylorโs Formula for Polynomials -- 5 Gaussโs 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-Taylorโs Formula for Formal Power Series and Heineโs Binomial Formula -- 9 Two Eulerโs Identities and Two q-Exponential Functions -- 10 q-Trigonometrie Functions -- 11 Jacobiโs Triple Product Identity -- 12 Classical Partition Function and Eulerโs Product Formula -- 13 q-Hypergeometric Functions and Heineโs Formula -- 14 More on Heineโs 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