Download e-book for kindle: A Comprehensive Treatment of q-Calculus by Thomas Ernst
By Thomas Ernst
To date, the theoretical improvement of q-calculus has rested on a non-uniform foundation. typically, the cumbersome Gasper-Rahman notation used to be used, however the released works on q-calculus seemed diversified counting on the place and through 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 way of introducing a brand new and engaging notation for q-calculus according to logarithms.For example, q-hypergeometric features are actually 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 features and the q-gamma functionality, whatever that in the past has been overlooked.
The booklet covers many issues on q-calculus, together with unique services, combinatorics, and q-difference equations. except a radical assessment of the ancient improvement of q-calculus, this publication additionally offers the domain names of recent physics for which q-calculus is appropriate, reminiscent of particle physics and supersymmetry, to call only a few.
Read or Download A Comprehensive Treatment of q-Calculus PDF
Similar number theory books
Because the first variation of this ebook was once released numerous new advancements were made within the box of the moiré idea. an important of those predicament new effects that experience lately been bought on moiré results among correlated aperiodic (or random) buildings, a subject matter that used to be thoroughly absent within the first version, and which seems now for the 1st time in a moment, separate quantity.
The concept that of the Euclidean simplex is critical within the examine of n-dimensional Euclidean geometry. This publication introduces for the 1st time the idea that of hyperbolic simplex as a huge thought in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the writer crafted gyrolanguage, the algebraic language that sheds typical mild on hyperbolic geometry and precise relativity.
The full fact approximately entire Numbers is an advent to the sector of quantity thought for college students in non-math and non-science majors who've studied no less than years of highschool algebra. instead of giving short introductions to a wide selection of themes, this publication presents an in-depth creation to the sector of quantity concept.
Top numbers are the multiplicative construction blocks of traditional numbers. realizing their total impression and particularly their distribution provides upward push to imperative questions in arithmetic and physics. specifically their finer distribution is heavily attached with the Riemann speculation, an important unsolved challenge within the mathematical international.
- Quadrangular Algebras. (MN-46) (Mathematical Notes)
- Complex Analysis: In the Spirit of Lipman Bers: 245 (Graduate Texts in Mathematics)
- Surveys in Number Theory (Developments in Mathematics)
- Posn(R) and Eisenstein Series (Lecture Notes in Mathematics)
Additional resources for A Comprehensive Treatment of q-Calculus
A Comprehensive Treatment of q-Calculus by Thomas Ernst