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A Mock Theta Function of Second Order

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  • Bhaskar Srivastava

Abstract

We consider the second-order mock theta function 𠒟 5 ( 𠑞 ), 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 𠒟 5 ( 𠑞 ) outside the unit circle is a theta function and also write ℎ 1 ( 𠑞 ) as a coefficient of 𠑧 0 of a theta series. First writing ℎ 1 ( 𠑞 ) as a coefficient of a theta function, we prove an identity for ℎ 1 ( 𠑞 ) .

Suggested Citation

  • Bhaskar Srivastava, 2009. "A Mock Theta Function of Second Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-15, April.
    • Handle: RePEc:hin:jijmms:978425
    DOI: 10.1155/2009/978425
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