Relevant bibliographies by topics / Jacobi triple product identity

Academic literature on the topic 'Jacobi triple product identity'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Jacobi triple product identity"

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Ewell, John A. "Consequences of a sextuple-product identity." International Journal of Mathematics and Mathematical Sciences 10, no. 3 (1987): 545–49. http://dx.doi.org/10.1155/s0161171287000656.

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A sextuple-product identity, which essentially results from squaring the classical Gauss-Jacobi triple-product identity, is used to derive two trigonometrical identities. Several special cases of these identities are then presented and discussed.
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2

Wenchang, Chu. "Durfee rectangles and the Jacobi triple product identity." Acta Mathematica Sinica 9, no. 1 (March 1993): 24–26. http://dx.doi.org/10.1007/bf02559979.

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3

Chan, Hei-Chi. "Another simple proof of the quintuple product identity." International Journal of Mathematics and Mathematical Sciences 2005, no. 15 (2005): 2511–15. http://dx.doi.org/10.1155/ijmms.2005.2511.

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4

SCZECH, Robert. "Gaussian sums, Dedekind sums and the Jacobi triple product identity." Kyushu Journal of Mathematics 49, no. 2 (1995): 233–41. http://dx.doi.org/10.2206/kyushujm.49.233.

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5

Jun-Ming Zhu. "A Semi-Finite Proof of Jacobi′s Triple Product Identity." American Mathematical Monthly 122, no. 10 (2015): 1008. http://dx.doi.org/10.4169/amer.math.monthly.122.10.1008.

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6

Srivastava, Hari M., M. P. Chaudhary, and Sangeeta Chaudhary. "Some Theta-Function Identities Related to Jacobi’s Triple-Product Identity." European Journal of Pure and Applied Mathematics 11, no. 1 (January 30, 2018): 1. http://dx.doi.org/10.29020/nybg.ejpam.v11i1.3222.

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The main object of this paper is to present some q-identities involving some of the theta functions of Jacobi and Ramanujan. These q-identities reveal certain relationships among three of the theta-type functions which arise from the celebrated Jacobi’s triple-product identity in a remarkably simple way. The results presented in this paper are motivated by some recent works by Chaudhary et al. (see [4] and [5]) and others (see, for example, [1] and [13]).
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Bhargava, S., Chandrashekar Adiga, and M. S. Mahadeva Naika. "QUINTUPLE PRODUCT IDENTITY AS A SPECIAL CASE OF RAMANUJAN'S 1ψ1 SUMMATION FORMULA." Asian-European Journal of Mathematics 04, no. 01 (March 2011): 31–34. http://dx.doi.org/10.1142/s1793557111000046.

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In this note we observe an interesting fact that the well-known quintuple product identity can be regarded as a special case of the celebrated 1ψ1 summation formula of Ramanujan which is known to unify the Jacobi triple product identity and the q -binomial theorem.
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8

Cooper, Shaun. "A new proof of the Macdonald identities for An−1." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 3 (June 1997): 345–60. http://dx.doi.org/10.1017/s1446788700001051.

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AbstractA new, elementary proof of the Macdonald identities for An−1 using induction on n is given. Specifically, the Macdonald identity for An is deduced by multiplying the Macdonald identity for An−1 and n Jacobi triple product identities together.
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9

Chaudhary, Mahendra. "A family of theta-function identities based upon Rα,Rβ and Rm-functions related to Jacobi’s triple-product identity." Publications de l'Institut Math?matique (Belgrade) 108, no. 122 (2020): 23–32. http://dx.doi.org/10.2298/pim2022023c.

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We establish a set of two new relationships involving R?,R? and Rm-functions, which are based on Jacobi?s famous triple-product identity. We, also provide answer for an open problem of Srivastava, Srivastava, Chaudhary and Uddin, which suggest to find an inter-relationships between R?,R? and Rm(m ? N), q-product identities and continued-fraction identities.
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10

DUVERNEY, DANIEL. "Some arithmetical consequences of Jacobi's triple product identity." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 3 (November 1997): 393–99. http://dx.doi.org/10.1017/s0305004197001916.

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Books on the topic "Jacobi triple product identity"

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An invitation to q-series: From Jacobi's triple product identity to Ramanujan's "most beautiful identity". Singapore: World Scientific Pub Co., 2011.

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Book chapters on the topic "Jacobi triple product identity"

1

Kac, Victor, and Pokman Cheung. "Jacobi’s Triple Product Identity." In Quantum Calculus, 35–36. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_11.

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Wilf, Herbert S. "The Number-Theoretic Content of the Jacobi Triple Product Identity." In The Andrews Festschrift, 227–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56513-7_11.

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3

"The Jacobi Triple Product Identity." In Monographs in Number Theory, 44–55. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813223370_0006.

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"Some applications of Jacobi's Triple Product Identity." In An Invitation to Q-Series, 21–29. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814343855_0004.

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"1 An introduction to Jacobi’s triple product identity." In Theta functions, elliptic functions and π, 1–14. De Gruyter, 2020. http://dx.doi.org/10.1515/9783110541915-001.

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"5 Elliptic functions and Jacobi’s triple product identity." In Theta functions, elliptic functions and π, 53–62. De Gruyter, 2020. http://dx.doi.org/10.1515/9783110541915-005.

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"Jacobi's Triple Product Identity: First proof (via functional equation)." In An Invitation to Q-Series, 5–9. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814343855_0002.

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8

"Ismail’s Proof of the ₁𝜓₁-Summation and Jacobi’s Triple Product Identity." In 𝑞-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra, 115. Providence, Rhode Island: American Mathematical Society, 1986. http://dx.doi.org/10.1090/cbms/066/13.

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9

"2 Jacobi’s theta functions of one variable and the triple product identity." In Theta functions, elliptic functions and π, 15–28. De Gruyter, 2020. http://dx.doi.org/10.1515/9783110541915-002.

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10

"Jacobi's Triple Product Identity: Second proof (via Gaussian polynomials and the q-binomial theorem)." In An Invitation to Q-Series, 11–20. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814343855_0003.

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