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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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| 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 |
| id | doaj-art-8b03ebdfbf3f409bb27db05309187014 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |