Transformation Formula of the “2nd” Order Mock Theta Function
نویسنده
چکیده
KAZUHIRO HIKAMI A. We give a transformation formula for the " 2nd order " mock theta function D 5 (q) = ∞ n=0 (−q) n (q; q 2) n+1 q n which was recently proposed in connection with the quantum invariant for the Seifert manifold.
منابع مشابه
Ramanujan’s Radial Limits
Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q approaches an even order 2k root of unity, that we have f(q)− (−1)(1− q)(1− q)(1− q) · · · ` 1− 2q + 2q − · · · ́ = O(1). We give two proofs of this claim by offering exact formulas for these limiting valu...
متن کاملAn Extension of the Hardy-ramanujan Circle Method and Applications to Partitions without Sequences
We develop a generalized version of the Hardy-Ramanujan “circle method” in order to derive asymptotic series expansions for the products of modular forms and mock theta functions. Classical asymptotic methods (including the circle method) do not work in this situation because such products are not modular, and in fact, the “error integrals” that occur in the transformations of the mock theta fu...
متن کاملAN EXTENSION OF THE HARDY-RAMANUJAN CIRCLE METHOD AND APPLICATIONS TO PARTITIONS WITHOUT SEQUENCES By KATHRIN BRINGMANN and KARL MAHLBURG
We develop a generalized version of the Hardy-Ramanujan “circle method” in order to derive asymptotic series expansions for the products of modular forms and mock theta functions. Classical asymptotic methods (including the circle method) do not work in this situation because such products are not modular, and in fact, the “error integrals” that occur in the transformations of the mock theta fu...
متن کاملJACOBI’S TRIPLE PRODUCT, MOCK THETA FUNCTIONS, AND THE q-BRACKET
In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...
متن کاملJACOBI’S TRIPLE PRODUCT, MOCK THETA FUNCTIONS, UNIMODAL SEQUENCES AND THE q-BRACKET
In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008