q-derivative
Sign in to saveIn mathematics, in the area of combinatorics and quantum calculus, the '''q-derivative, or Jackson derivative', is a q''-analog of the ordinary derivative, introduced by Frank Hilton Jackson. It is the inverse of Jackson's q-integration. For other forms of q-derivative, see .
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Article
11 sectionsContents
- Definition
- Relationship to ordinary derivatives
- Higher order ''q''-derivatives
- Generalizations
- Post Quantum Calculus
- Hahn difference
- ''β''-derivative
- Applications
- See also
- Citations
- Bibliography
In mathematics, in the area of combinatorics and quantum calculus, the '''q-derivative, or Jackson derivative', is a q''-analog of the ordinary derivative, introduced by Frank Hilton Jackson. It is the inverse of Jackson's q-integration. For other forms of q-derivative, see .
==Definition== The q-derivative of a function f(x) is defined as \left(\frac{d}{dx}\right)_q f(x)=\frac{f(qx)-f(x)}{qx-x}.
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