By Thomas Ernst
To date, the theoretical improvement of q-calculus has rested on a non-uniform foundation. often, the cumbersome Gasper-Rahman notation was once used, however the released works on q-calculus regarded various looking on the place and by means of whom they have been written. This confusion of tongues not just advanced the theoretical improvement but additionally contributed to q-calculus final a overlooked mathematical box. This ebook overcomes those difficulties by means of introducing a brand new and fascinating notation for q-calculus in line with logarithms.For example, q-hypergeometric capabilities are actually visually transparent and straightforward to track again to their hypergeometric mom and dad. With this new notation it's also effortless to work out the relationship among q-hypergeometric features and the q-gamma functionality, whatever that in the past has been overlooked.
The ebook covers many issues on q-calculus, together with distinctive features, combinatorics, and q-difference equations. except a radical evaluation of the ancient improvement of q-calculus, this booklet additionally provides the domain names of contemporary physics for which q-calculus is appropriate, comparable to particle physics and supersymmetry, to call only a few.
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A Comprehensive Treatment of q-Calculus by Thomas Ernst