PARTIAL SECOND ORDER MOCK THETA FUNCTIONS, THEIR EXPANSIONS AND PADE APPROXIMANTS
نویسندگان
چکیده
منابع مشابه
On Two Fifth Order Mock Theta Functions
We consider the fifth order mock theta functions χ0 and χ1, defined by Ramanujan, and find identities for these functions, which relate them to indefinite theta functions. Similar identities have been found by Andrews for the other fifth order mock theta functions and the seventh order functions.
متن کاملThe Tenth Order Mock Theta Functions Revisited
In this paper we consider the first four of the eight identities between the tenth order mock theta functions, found in Ramanujan’s lost notebook. These were originally proved by Choi. Here we give an alternative proof.
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We study the applicability of Pade Approximants (PA) to estimate a ”sum” of asymptotic series of the type appearing in QCD. We indicate that one should not expect PA to converge for positive values of the coupling constant and propose to use PA for the Borel transform of the series. If the latter has poles on the positive semiaxis, the Borel integral does not exist, but we point out that the Ca...
متن کاملAsymptotic 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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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2007
ISSN: 0304-9914
DOI: 10.4134/jkms.2007.44.4.767