CERTAIN RELATIONS FOR MOCK THETA FUNCTIONS OF ORDER EIGHT
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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In 2004, the first author gave the combinatorial interpretations of four mock theta functions of Srinivasa Ramanujan using n-color partitions which were introduced by himself and G.E. Andrews in 1987. In this paper we introduce a new class of partitions and call them “split (n+t)-color partitions”. These new partitions generalize Agarwal–Andrews (n + t)-color partitions. We use these new combin...
متن کاملRamanujan's mock theta functions.
In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268-277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite...
متن کاملEffective Congruences for Mock Theta Functions
LetM(q) = ∑ c(n)q be one of Ramanujan’s mock theta functions. We establish the existence of infinitely many linear congruences of the form:
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2009
ISSN: 1225-1763
DOI: 10.4134/ckms.2009.24.4.629