Abstract
In ordinary calculus, a derivative is defined as the limit of a ratio, and a definite integral is defined as the limit of an infinite sum. Their subtle and surprising relation is given by the Newton-Leibniz formula, also called the fundamental theorem of calculus. In contrast, since the introduction of the definite q-integral has been motivated by an antiderivative, the relation between the q-derivative and definite q-integral is more obvious. Analogous to the ordinary case, we have the following fundamental theorem, or Newton-Leibniz formula, for q-calculus.
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© 2002 Victor Kac.
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Kac, V., Cheung, P. (2002). Fundamental Theorem of q-Calculus and Integration by Parts. In: Quantum Calculus. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0071-7_20
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DOI: https://doi.org/10.1007/978-1-4613-0071-7_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95341-0
Online ISBN: 978-1-4613-0071-7
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