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Математические заметки, 2022, том 112, выпуск 5, статья опубликована в англоязычной версии журнала
(Mi mzm13788)
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Статьи, опубликованные в английской версии журнала
Jacobi's Triple-Product Identity
and an Associated Family of Theta-Function Identities
H. M. Srivastavaabcd, M. P. Chaudharye, S. Chaudharyf, G. A. Salilewg a Department of Mathematics and Statistics,
University of Victoria,
Victoria, British Columbia, V8W 3R4 Canada
b Department of Medical Research, China Medical
University Hospital,
China Medical University,
Taichung, 40402 Taiwan
c Section of Mathematics,
International Telematic University Uninettuno, Rome, I-00186 Italy
d Department of Mathematics and Informatics,
Azerbaijan University,
Baku, AZ1007 Azerbaijan
e Department of Mathematics, Netaji Subhas University of Technology,
New Delhi, 110078 India
f School of Computer and System Sciences,
Jawaharlal Nehru University,
New Delhi, 110067 India
g Department of Mathematics,
Debark University,
Debark,
North Gondar Zone,
Ethiopia
Аннотация:
The main object of this paper is to present a family of
$q$-series
identities which involve some of the theta functions of Jacobi and
Ramanujan.
Each of these (presumably new)
$q$-series identities reveals
interesting relationships among three of the theta-type functions which
stem from the celebrated Jacobi's triple-product identity in a remarkably
simple way.
The results presented in this paper are motivated essentially
by a number of recent works dealing with the subject matter
which is investigated herein.
Ключевые слова:
theta-function identities,
Jacobi's triple-product identity,
Ramanujan's theta functions,
$q$-series identities,
quadratic forms and elliptic functions,
number theory and the theory of partitions.
Поступило: 01.12.2020 Исправленный вариант: 22.06.2022
Образец цитирования:
H. M. Srivastava, M. P. Chaudhary, S. Chaudhary, G. A. Salilew, “Jacobi's Triple-Product Identity
and an Associated Family of Theta-Function Identities”, Math. Notes, 112:5 (2022), 755–762
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