Quantum CalculusSpringer Science & Business Media, 16 nov. 2001 - 112 pages 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 inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by Professor Kac over the last few years at MIT. |
Table des matières
II | 1 |
III | 5 |
IV | 7 |
V | 12 |
VI | 14 |
VII | 17 |
VIII | 21 |
IX | 27 |
XVIII | 56 |
XIX | 60 |
XX | 64 |
XXI | 67 |
XXII | 73 |
XXIII | 76 |
XXIV | 80 |
XXV | 85 |
XI | 29 |
XII | 33 |
XIII | 35 |
XIV | 37 |
XV | 43 |
XVI | 47 |
XVII | 50 |
XXVI | 90 |
XXVII | 92 |
XXVIII | 99 |
XXIX | 106 |
XXX | 109 |
| 111 | |
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Expressions et termes fréquents
a)m+n analytic function antiderivative apply ax³ Bernoulli numbers Bernoulli polynomials binomial formula Bn(x Bq(t chapter coefficient of q compute congruent converges Cosq define definite q-integral Dqf(x equation Euler-Maclaurin formula Euler's product example exponential function expression f(qx f(x)dqx finite formal power series formula 8.1 function f(x fundamental theorem ƒ q³ geometric series Heine's binomial formula Heine's formula Hence hypergeometric series induction infinite sums j-dimensional subspace Jackson formula Jackson integral left-hand side linear operator modulo Newton-Leibniz formula nonnegative integer number theory obtain ordinary calculus partition Pn(x positive integer product formula Proof Proposition q-analogue q-binomial coefficients q-derivative q-exponential q-gamma function q-Taylor qm+n quantum calculus quotient rule right-hand side sequence of polynomials similar square numbers Taylor expansion Taylor formula Taylor's formula Theorem 2.1 triangular numbers unique vanish zero