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Theta function identities and vanishing coefficient results for continued fractions of order sixty-four

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Abstract

Eight continued fractions of order sixty-four are derived from a general continued fraction identity of Ramanujan. A general theta-function identity is proved for the eight continued fractions and partition-theoretic results are obtained therefrom. Some vanishing coefficient arising for the continued fractions and their reciprocals are also offered.

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References

  1. N. D. Baruah and M. Kaur: Some results on vanishing coefficients in infinite product expansions, Ramanujan J. 53 (2020), 551–568.

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  2. B. C. Berndt: Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991.

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  3. M. D. Hirschhorn: Two remarkable q-series expansions. Ramanujan J. 49(2) (2018), 451–463.

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Acknowledgements

The authors are grateful to the referee, who read our manuscript with great care and offered useful suggestions. The first author acknowledges the financial support received from the Department of Science and Technology (DST), Government of India through INSPIRE Fellowship [DST/INSPIRE Fellowship/2021 /IF210210].

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, 791112, India

    Shraddha Rajkhowa & Nipen Saikia

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  1. Shraddha Rajkhowa
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  2. Nipen Saikia
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Correspondence to Nipen Saikia.

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Communicated by Eknath Ghate.

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Rajkhowa, S., Saikia, N. Theta function identities and vanishing coefficient results for continued fractions of order sixty-four. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00555-x

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  • DOI: https://doi.org/10.1007/s13226-024-00555-x

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