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 assorted reckoning on the place and via whom they have been written. This confusion of tongues not just advanced the theoretical improvement but in addition contributed to q-calculus closing a overlooked mathematical box. This publication overcomes those difficulties by means of introducing a brand new and fascinating notation for q-calculus in line with logarithms.For example, q-hypergeometric services are actually visually transparent and straightforward 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, whatever that in the past has been overlooked.

The booklet covers many subject matters on q-calculus, together with precise features, combinatorics, and q-difference equations. except a radical assessment of the old improvement of q-calculus, this booklet additionally provides the domain names of recent physics for which q-calculus is appropriate, corresponding to particle physics and supersymmetry, to call only a few.

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