| Тета-функция Рамануджана |  |
Тета-функция Рамануджана обобщает тета-функции Якоби, не разрушая основные их свойства. В частности, тройное произведение Якоби принимает особенно элегантный вид, когда записывается в терминах тета-функции Рамануджана. Функция носит имя Сриниваса... Википедия
Ramanujan's general theta function f (a,b) is defined by f (a,b) := ∞. X n=−∞ an(n+1)/2bn(n−1)/2,. |ab| < 1. Page 6. Definitions. Definition. Ramanujan's ... |
In terms of f(a, b) Ramanujan's one variable theta function is f(−q) = f(−q, −q2), which perhaps explains why Ramanujan used f(−q) instead of the more obvious. |
21 дек. 2021 г. · Not only did Ramanujan enjoy calculating special values of individual theta functions, but he also had a marvellous insight for finding certain ... |
In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. |
A mock theta function is a function f of the complex variable q, defined by a q-series of a particular type (Ramanujan calls this the Eulerian form) |
Ramanujan gives no definition of mock theta functions but only a list of 17 examples and a qualitative description of the key property that he had noticed: ... |
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