By Thomas Ernst
To date, the theoretical improvement of q-calculus has rested on a non-uniform foundation. mostly, the cumbersome Gasper-Rahman notation was once 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 complex the theoretical improvement but in addition contributed to q-calculus final a ignored mathematical box. This ebook overcomes those difficulties by means of introducing a brand new and engaging notation for q-calculus in accordance 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, anything that previously has been overlooked.
The e-book covers many issues on q-calculus, together with exact capabilities, combinatorics, and q-difference equations. except an intensive evaluate of the old 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.
Read Online or Download A Comprehensive Treatment of q-Calculus PDF
Similar number theory books
Within the Nineteen Seventies Hirzebruch and Zagier produced elliptic modular types with coefficients within the homology of a Hilbert modular floor. They then computed the Fourier coefficients of those varieties when it comes to interval integrals and L-functions. during this publication the authors take another method of those theorems and generalize them to the environment of Hilbert modular kinds of arbitrary measurement.
During this textual content, the well-known zeros of the Riemann zeta functionality and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed via numerous zeta features outfitted over these zeros.
This quantity includes unique examine articles, survey articles and lecture notes regarding the Computations with Modular kinds 2011 summer time tuition and convention, held on the collage of Heidelberg. A key subject matter of the convention and summer time tuition used to be the interaction among idea, algorithms and scan.
Posn(R) and Eisenstein sequence offers an creation, requiring minimum necessities, to the research on symmetric areas of optimistic sure actual matrices in addition to quotients of this house through the unimodular workforce of necessary matrices. The method is gifted in very classical phrases and contains fabric on specific capabilities, significantly gamma and Bessel capabilities, and makes a speciality of definite mathematical elements of Eisenstein sequence.
Additional resources for A Comprehensive Treatment of q-Calculus
A Comprehensive Treatment of q-Calculus by Thomas Ernst