The Power of q (Record no. 427118)
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| 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 |
| -- | |
| -- | 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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