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Bruce C.Berndt — Ramanujan's Notebooks (part 4)
Bruce C.Berndt — Ramanujan's Notebooks (part 4)



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Название: Ramanujan's Notebooks (part 4)

Автор: Bruce C.Berndt

Аннотация:

During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 451

Добавлена в каталог: 30.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Tauberian theorems      61—62 118—119 395—396
Telescoping product      396 398—399
Telescoping series      393 396—398
Thandapani, E.      35
Theta transformation formula      270
Theta-functions      78 423—426
Thoreau, H.D.      1
Triangular numbers      110
Trigonometric identities      32—34 39 183—184
Trinity College, Cambridge      6
Uchimura, K.      265
Valence formula      239
Van den Berg, F.J.      85
Vandermonde's theorem      346
Venkatachaliengar, K.      6 172
Viete, F.      12
von Staudt-Clausen theorem      75
Wagstaff Jr., S.S.      6
Waldschmidt, M.      91
Watson's lemma      293 312
Watson's q-analogue of Whipple's theorem      156
Watson, G.N.      1 342—343
Weierstrass $\mathscr{P}$-function      249—250 260
Weierstrass normal form      249—250 258—259
Weierstrass theory      248—251 258—260
Wheeler, F.      6
Whipple's theorem, ij-analogue      155—156
Widder, D.V.      331—332
Wiener, N.      396
Wigert, S.      87
Williams, K.S.      3 6 62 71—72
Wintner, A.      62
Wolfram, S.      7 140
Wright, E.M.      56—58 70 108 383
Yao, Q.      135
Young, J.      134
Zagier, D.      137 286
Zhang, L.-C.      6 139 176
Zhang, W.B.      6
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