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The Power of q (Record no. 427118)

MARC details
000 -LEADER
fixed length control field 05572nam a22004695i 4500
020 ## - INTERNATIONAL STANDARD BOOKNUMBER
International Standard Book Number 9783319577623
-- 978-3-319-57762-3
024 7# -
-- 10.1007/978-3-319-57762-3
-- doi
040 ## -
-- ISI Library, Kolkata
050 #4 -
-- QA241-247.5
072 #7 -
-- PBH
-- bicssc
072 #7 -
-- MAT022000
-- bisacsh
072 #7 -
-- PBH
-- thema
082 04 - DEWEYDECIMAL CLASSIFICATION NUMBER
Classification number 512.7
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Hirschhorn, Michael D.
Relator code aut
-- http://id.loc.gov/vocabulary/relators/aut
245 14 - TITLE STATEMENT
Title The Power of q
Medium [electronic resource] :
Remainder of title A Personal Journey /
Statement of responsibility, etc by Michael D. Hirschhorn.
942 ## - ADDED ENTRY ELEMENTS(KOHA)
Koha item type E-BOOKS
100 1# - MAIN ENTRY--PERSONAL NAME
-- author.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE STATEMENTS
Place of production, publication, distribution, manufacture Cham :
Name of producer, publisher, distributor, manufacturer Springer International Publishing :
-- Imprint: Springer,
Date of production, publication, distribution, manufacture 2017.
300 ## -
-- XXIV, 415 p.
-- online resource.
336 ## - CONTENT TYPE
Content Type Term text
Content Type Code txt
Source rdacontent
337 ## - MEDIA TYPE
Media Type Term computer
Media Type Code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier Type Term online resource
Carrier Type Code cr
Source rdacarrier
347 ## -
-- text file
-- PDF
-- rda
490 1# -
-- Developments in Mathematics,
-- 1389-2177 ;
-- 49
505 0# -
-- Foreword -- Preface -- 1. Introduction -- 2. Jacobi's two-squares and four-squares theorems -- 3. Ramanujan's partition congruences -- 4. Ramanujan's partition congruences— a uniform proof -- 5. Ramanujan's "most beautiful identity" -- 6. Ramanujan's partition congruences for powers of 5 -- 7. Ramanujan's partition congruences for powers of 7 -- 8. Ramanujan's 5-dissection of Euler's product -- 9. A "difficult and deep" identity of Ramanujan -- 10. The quintuple product identity -- 11. Winquist's identity -- 12. The crank of a partition -- 13. Two more proofs of p(11n + 6) ≡ 0 (mod 11), and more -- 14. Partitions where even parts come in two colours -- 15. The Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction -- 16. The series expansion of the Rogers–Ramanujan continued fraction -- 17. The 2- and 4-dissections of Ramanujan’s continued fraction and its reciprocal -- 18. The series expansion of the Ramanujan-Gollnitz-Gordon continued fraction and its reciprocal -- 19. Jacobi’s “aequatio identica satis abstrusa” -- 20. Two modular equations -- 21. A letter from Fitzroy House -- 22. The cubic functions of Borwein, Borwein and Garvan -- 23. Some classical results on representations -- 24. Further classical results on representations -- 25. Further results on representations -- 26. Even more representation results -- 27. Representation results and Lambert series -- 28. The Jordan–Kronecker identity -- 29. Melham’s identities -- 30. Partitions into four squares -- 31. Partitions into four distinct squares of equal parity -- 32. Partitions with odd parts distinct -- 33. Partitions with even parts distinct -- 34. Some identities involving phi(q) and  psi(q) -- 35. Some useful parametrisations -- 36. Overpartitions -- 37. Bipartitions with odd parts distinct -- 38. Overcubic partitions -- 39. Generalised Frobenius partitions -- 40. Some modular equations of Ramanujan -- 41. Identities involving k = qR(q)R(q2)2 -- 42. Identities involving v=q1/2(q,q7;q8)infinity/(q3,q5;q8)infinity -- 43. Ramanujan's tau function -- Appendix -- Index.
520 ## -
-- This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction, the famous “forty identities” of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a “mysterious” partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper “which even Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.
650 #0 -
-- Number theory.
650 14 -
-- Number Theory.
-- http://scigraph.springernature.com/things/product-market-codes/M25001
710 2# -
-- SpringerLink (Online service)
773 0# -
-- Springer eBooks
776 08 -
-- Printed edition:
-- 9783319577616
776 08 -
-- Printed edition:
-- 9783319577630
776 08 -
-- Printed edition:
-- 9783319862415
830 #0 -
-- Developments in Mathematics,
-- 1389-2177 ;
-- 49
856 40 -
-- https://doi.org/10.1007/978-3-319-57762-3
912 ## -
-- ZDB-2-SMA
950 ## -
-- Mathematics and Statistics (Springer-11649)

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