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The Fourth and Eighth Order Mock Theta Functions
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In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to a2. I presume they will be helpful in getting fundamental transformations.
Abstract
In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to a2. I presume they will be helpful in getting fundamental transformations.
참고문헌 (8)
- G. E. Andrews, "The fth and seventh order mock theta functions", Trans. Amer. Math. Soc., 293, pp.113~134 (1986)
- G. E. Andrews, "Ramanujan's \ Lost" Notebook VII: The sixth order mock theta functions", Adv. in Math., 89, pp.60~105 (1991)
- D. Hickerson, "A proof of mock theta conjectures", Inven. Math., 94, pp.639~660 (1998)
- D. Hickerson, "On the seventh order mock theta functions", Inven. Math., 94, pp.661~677 (1988)
- K. Hikami, "Mock (false) theta functions as quantum invariants", Regular and Chaotic Dynamics, 10, pp.509~530 (2005)
- S. Ramanujan, "Collected Papers" (1962), Chelsea
- G. N. Watson, "The nal problem: An account of the mock theta functions", J. London Math. Soc., 11, pp.55~80 (1936)
- S. Zwegers, "On two fth order mock theta functions", The Ramanujan Journal
관련 논문AI추천
Certain relations for mock theta functions of order eightMaheshwar Pathak, Pankaj Srivastava대한수학회 · 대한수학회논문집2009 · 제24권 제4호New indefinite theta series expressions for some even-order mock theta functionsQiuxia Hu, Zeya Jia대한수학회 · 대한수학회보2025 · 제62권 제6호A Note on Certain Properties of Mock Theta Functions of Order EightAnwar Jahan Wahidi, Pankaj Srivastava경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제2호On four new mock theta functionsQiuXia Hu대한수학회 · 대한수학회보2020 · 제57권 제2호Structural insights into mock theta-function identities via multivariable R-functions and partition theoryArooj Fatima, SERKAN ARACI장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제4호New identities for ratios of Ramanujan’s theta functionK. Sushan Bairy, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호
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