On some new Bailey pairs and new expansions for some mock theta functions
نویسندگان
چکیده
منابع مشابه
New combinatorial interpretations of some mock theta functions
In 1972, Bender and Knuth established a bijection between certain infinite matrices of non-negative integers and plane partitions and in [2] a bijection between Bender-Knuth matrices and n-color partitions was shown. Here we use this later bijection and translate the recently found n-color partition theoretic interpretations of four mock theta functions of S. Ramanujan in [1] to new combinatori...
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Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain c...
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Some Mock Theta functions have been interpreted in terms of n-color partition. In this paper we use a new technique to gain a deeper insight on these interpretations, as well as we employ this new technique to obtain in a more systematic way similar new interpretations for three other mock theta functions. keywords: mock theta functions, n-color partitions, combinatorial interpretations, modula...
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This study began in an effort to find a simpler derivation of the Bailey pairs associated with the seventh order mock theta functions. It is shown that the introduction of a new parameter independent of both a and q leads to a much simpler treatment. It is noted that a previous treatment of the central fifth order mock theta function inadvertently uses this approach. The paper concludes by appl...
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Let (αn(a, k), βn(a, k)) be a WP-Bailey pair. Assuming the limits exist, let (α n(a), β ∗ n(a)) = lim k→1 ( αn(a, k), βn(a, k) 1− k ) be the derived WP-Bailey pair. By considering a particular limiting case of a transformation due to George Andrews, we derive some transformation and summation formulae for derived WP-Bailey pairs. We then use the formula to derive new identities for various thet...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2016
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2016.v23.n2.a4