A Mock Theta Function of Second Order

We consider the second-order mock theta function 𝒟5 (𝑞), which Hikami came across in his work on mathematical physics and quantum invariant of three manifold. We give their bilateral form, and show that it is the same as bilateral third-order mock theta function of Ramanujan. We also show that the m...

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Main Author: Bhaskar Srivastava
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2009/978425
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author Bhaskar Srivastava
author_facet Bhaskar Srivastava
author_sort Bhaskar Srivastava
collection DOAJ
description We consider the second-order mock theta function 𝒟5 (𝑞), which Hikami came across in his work on mathematical physics and quantum invariant of three manifold. We give their bilateral form, and show that it is the same as bilateral third-order mock theta function of Ramanujan. We also show that the mock theta function 𝒟5 (𝑞) outside the unit circle is a theta function and also write ℎ1(𝑞) as a coefficient of 𝑧0 of a theta series. First writing ℎ1(𝑞) as a coefficient of a theta function, we prove an identity for ℎ1(𝑞).
format Article
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institution Kabale University
issn 0161-1712
1687-0425
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publishDate 2009-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-8b03ebdfbf3f409bb27db053091870142025-08-20T03:37:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/978425978425A Mock Theta Function of Second OrderBhaskar Srivastava0Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, IndiaWe consider the second-order mock theta function 𝒟5 (𝑞), which Hikami came across in his work on mathematical physics and quantum invariant of three manifold. We give their bilateral form, and show that it is the same as bilateral third-order mock theta function of Ramanujan. We also show that the mock theta function 𝒟5 (𝑞) outside the unit circle is a theta function and also write ℎ1(𝑞) as a coefficient of 𝑧0 of a theta series. First writing ℎ1(𝑞) as a coefficient of a theta function, we prove an identity for ℎ1(𝑞).http://dx.doi.org/10.1155/2009/978425
spellingShingle Bhaskar Srivastava
A Mock Theta Function of Second Order
International Journal of Mathematics and Mathematical Sciences
title A Mock Theta Function of Second Order
title_full A Mock Theta Function of Second Order
title_fullStr A Mock Theta Function of Second Order
title_full_unstemmed A Mock Theta Function of Second Order
title_short A Mock Theta Function of Second Order
title_sort mock theta function of second order
url http://dx.doi.org/10.1155/2009/978425
work_keys_str_mv AT bhaskarsrivastava amockthetafunctionofsecondorder
AT bhaskarsrivastava mockthetafunctionofsecondorder