Asymptotic expansions of finite theta series
نویسندگان
چکیده
منابع مشابه
Asymptotic Expansions of Certain Partial Theta Functions
We establish an asymptotic expansion for a class of partial theta functions generalizing a result found in Ramanujan’s second notebook. Properties of the coefficients in this more general asymptotic expansion are studied, with connections made to combinatorics and a certain Dirichlet series.
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There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1977
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-32-2-129-146