In q-calculus, the original mathematical object is recovered by taking the limit as the parameter q tends to 1 of the q-analog.
Notes on verification
Four independent authoritative mathematical sources (Wikipedia, Springer, Wolfram MathWorld, and arXiv) all consistently confirm the same definition and limiting behavior of q-analogs. The sources include peer-reviewed academic materials and established mathematical references.
Sources
- Quantum calculus (en.wikipedia.org)
- https://mathworld.wolfram.com/q-Analog.html (mathworld.wolfram.com)
- https://arxiv.org/pdf/2008.11418 (arxiv.org)
- https://arxiv.org/pdf/1505.02179 (arxiv.org)
- https://link.springer.com/chapter/10.1007/978-3-0348-0431-8_1 (link.springer.com)
- https://www.researchgate.net/publication/331135938_SOME_NEW_RESULTS_IN_THE_Q_CALCULUS (researchgate.net)