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Author:   Michael D. Hirschhorn
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2017
Volume:   49
Weight:   7.804kg
ISBN:  

9783319577616

ISBN 10:   3319577611
Pages:   415
Publication Date:   16 August 2017
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

"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."

Reviews

“This book provides an introduction to q-series that would be accessible to calculus students, its main purpose is to offer beautiful theorems to the reader along with, in many instances, equally beautiful proofs that cannot be found elsewhere, except possibly in the author’s own papers. … those who already love q-series will find much to admire and enjoy in Hirschhorn’s book The Power of q. Those desiring an introduction to the subject can also enjoy it.” (Bruce Berndt, The American Mathematical Monthly, Vol. 126 (2), April, 2019)

This book provides an introduction to q-series that would be accessible to calculus students, its main purpose is to offer beautiful theorems to the reader along with, in many instances, equally beautiful proofs that cannot be found elsewhere, except possibly in the author's own papers. ... those who already love q-series will find much to admire and enjoy in Hirschhorn's book The Power of q. Those desiring an introduction to the subject can also enjoy it. (Bruce Berndt, The American Mathematical Monthly, Vol. 126 (2), April, 2019)

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