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On four new mock theta functions
On four new mock theta functions
논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제57권 제2호 KCI Accredited Journals
- 발행연도
- 2020.1
- 수록면
- 345 - 354 (10page)
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On four new mock theta functions
초록· 키워드
오류제보하기
In this paper, we first give some representations for four new mock theta functions defined by Andrews \cite{Andrews} and Bringmann, Hikami and Lovejoy \cite{BHL} using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of $_2\psi_2$ series \[\sum_{n=-\infty}^\infty\frac{(a,c;q)_n}{(b,d;q)_n}z^n\] and Ramanujan's sum \[\sum_{n=-\infty}^\infty\frac{(a;q)_n}{(b;q)_n}z^n.\]
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참고문헌 (13)
참고문헌 신청
George E. Andrews / 2012 / q-Orthogonal polynomials, Rogers-Ramanujan identities, and mock theta functions / Proceedings of the Steklov Institute of Mathematics 276(1):21~32
G. E. Andrews / 1991 / Ramanujan's "lost" notebook. VII. The sixth order mock theta functions / Adv. Math 89(1):60~105
N. Bagis / 2018 / Properties of Lerch sums and Ramanujan's mock theta functions / arXiv:1808. 07970v3 [math.GM]
W. N. Bailey / 1950 / On the basic bilateral hypergeometric series 2ψ2, Quart / J. Math., Oxford Ser 1:194~198
Kathrin Bringmann / 2011 / On the modularity of the unified WRT invariants of certain Seifert manifolds / Advances in Applied Mathematics 46(1-4):86~93
G. E. Andrews / 1991 / Ramanujan's "lost" notebook. VII. The sixth order mock theta functions / Adv. Math 89(1):60~105
N. Bagis / 2018 / Properties of Lerch sums and Ramanujan's mock theta functions / arXiv:1808. 07970v3 [math.GM]
W. N. Bailey / 1950 / On the basic bilateral hypergeometric series 2ψ2, Quart / J. Math., Oxford Ser 1:194~198
Kathrin Bringmann / 2011 / On the modularity of the unified WRT invariants of certain Seifert manifolds / Advances in Applied Mathematics 46(1-4):86~93
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