By Thomas Ernst

ISBN-10: 303480430X

ISBN-13: 9783034804301

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 regarded diverse looking on the place and by way of whom they have been written. This confusion of tongues not just advanced the theoretical improvement but additionally contributed to q-calculus ultimate a missed mathematical box. This publication overcomes those difficulties by way of introducing a brand new and fascinating notation for q-calculus according to logarithms.For example, q-hypergeometric capabilities 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 capabilities and the q-gamma functionality, whatever that earlier has been overlooked.

The booklet covers many issues on q-calculus, together with distinct services, combinatorics, and q-difference equations. except a radical overview of the old improvement of q-calculus, this ebook additionally offers the domain names of recent physics for which q-calculus is appropriate, corresponding to particle physics and supersymmetry, to call only a few.

**Read or Download A Comprehensive Treatment of q-Calculus PDF**

**Best number theory books**

**New PDF release: Number Theory for Computing (2nd Edition)**

Amazon: http://www. amazon. com/Number-Theory-Computing-Song-Yan/dp/3540430725

This e-book offers an exceptional creation to the classical trouble-free quantity conception and the fashionable algorithmic quantity idea, and their purposes in computing and data know-how, together with computers layout, cryptography and community safeguard. during this moment variation proofs of many theorems were supplied, additional additions and corrections have been made.

**New PDF release: Invitation to the Mathematics of Fermat-Wiles**

Assuming basically modest wisdom of undergraduate point math, Invitation to the math of Fermat-Wiles provides assorted ideas required to understand Wiles' awesome evidence. additionally, it locations those innovations of their old context. This e-book can be utilized in advent to arithmetic theories classes and in exact themes classes on Fermat's final theorem.

**Download e-book for kindle: Introduction to Cyclotomic Fields by Lawrence C. Washington**

Creation to Cyclotomic Fields is a gently written exposition of a principal zone of quantity idea that may be used as a moment path in algebraic quantity concept. beginning at an undemanding point, the quantity covers p-adic L-functions, type numbers, cyclotomic devices, Fermat's final Theorem, and Iwasawa's conception of Z_p-extensions, top the reader to an knowing of recent study literature.

**Additional resources for A Comprehensive Treatment of q-Calculus**

**Example text**

10. 11. 12. 13. the study of elliptic functions from the nineteenth century the development of theta functions additive analytic numbers theory, or theory of partitions the field of hypergeometric functions gamma function theory Bernoulli and Euler polynomials umbral calculus theory of finite differences combinatorics + q-binomial coefficient identities theory of finite fields + primitive roots Mock theta functions multiple hypergeometric functions elliptic integrals and Dedekind eta function The main trunk of the tree is the subject q.

Russian School: Russian mathematicians have greatly influenced the above mentioned Hungarian School through studies of polynomials. Russia has, in general, a strong tradition in mathematics, which dates back to Euler and the 18th century mathematicians who took up this heritage. Euler has very much contributed to the Proceedings of the St. Petersburg Academy. After his death, his successors could not keep the high level from before. Euler himself died in St. Petersburg, and it is a well-established fact that both his direct influence and also his unpublished papers and work remained in Russia, which explains in part the high level of mathematics in Russia.

In the footsteps of Nielsen, Niels Erik Nørlund (1885–1981) in the remarkable work [403] gave the first rigorous treatment of finite differences from the perspective of the mathematician. Nørlund gave lectures on hypergeometric series in Copenhagen until 1955. Nørlund also knew q-calculus; F. Ryde published a thesis on this subject under his supervision in Lund. The next link in the chain is perhaps Per Karlsson (1936–), the expert on multiple hypergeometric functions and friend, among other things, collaborator and model of the author.

### A Comprehensive Treatment of q-Calculus by Thomas Ernst

by David

4.5