The Power of q

512.7

Hirschhorn, Michael D. The Power of q A Personal Journey / by Michael D. Hirschhorn. -
XXIV, 415 p. online resource. - (Developments in Mathematics, 49) Content notes : 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. 9783319577623 * Number theory. Number Theory. * Series