By Thomas Ernst
To date, the theoretical improvement of q-calculus has rested on a non-uniform foundation. more often than not, the cumbersome Gasper-Rahman notation was once used, however the released works on q-calculus regarded various looking on the place and through whom they have been written. This confusion of tongues not just advanced the theoretical improvement but additionally contributed to q-calculus closing a overlooked mathematical box. This booklet overcomes those difficulties by means of introducing a brand new and fascinating notation for q-calculus in line with logarithms.For example, q-hypergeometric features at the moment are visually transparent and simple to track again to their hypergeometric mom and dad. With this new notation it's also effortless to determine the relationship among q-hypergeometric capabilities and the q-gamma functionality, anything that formerly has been overlooked.
The booklet covers many subject matters on q-calculus, together with unique features, combinatorics, and q-difference equations. except an intensive evaluate of the ancient improvement of q-calculus, this e-book additionally offers the domain names of recent physics for which q-calculus is acceptable, corresponding to particle physics and supersymmetry, to call only a few.
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