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: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0161-1712 1687-0425 |