Results 11 to 20 of about 3,558,031 (100)
Jacobi's triple product identity and theta function identities [PDF]
Mathematical Communications, 2011 As a unified approach, Jacobi's triple product identity will be utilized to derive theta function formulae due to Baruah-Berndt (2007), identities of Rogers--Ramanujan functions and modular equations due to Ramanujan.
Chu, Wenchang, Yan, Qinglun
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A Vanishing Finite Sum associated with Jacobi's triple product identity [PDF]
Journal of Combinatorial Theory, 1969 AbstractJacobi's triple product identity is shown to be equivalent to the vanishing of a finite sum. The vanishing of the sum is then established independently of Jacobi's identity, and the behavior of a related finite sum is discussed. Finally, the possibility of generalizing Jacobi's identity to include variables with non-quadratic exponents is ...
Stolarsky, Kenneth B.
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Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product
, 2022 Andrews and Merca investigated a truncated version of Euler's pentagonal number theorem and showed that the coefficients of the truncated series are nonnegative.
Liuquan Wang, Wang, Liuquan
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Jacobi's identity and the König-Egerváry theorem [PDF]
, 1984 The König-Egerváry theorem, which asserts that the maximum size of a partial matching in a relation equals the minimum size of a separating set, is proved using Jacobi's identity relating complementary minors in a matrix and its ...
Kung, Joseph P.S
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The multisection method for triple products and identities of Rogers–Ramanujan type [PDF]
, 2008 By applying the bisection and trisection method to Jacobi's triple product identity, we establish several identities factorizing sum and difference of infinite products, which lead, in turn, to new and elementary proofs for twenty identities of Rogers ...
Chu, Wenchang, Wang, Chenying, WANG C.
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The Triple Helix of University-Industry-Government Relations [PDF]
, 2012 Etzkowitz & Leydesdorff (2000) further elaborated the Triple Helix of University-Industry-Government Relations (cf. Etzkowitz & Leydesdorff, 1995; Lowe, 1982) into a model for studying knowledge-based economies.
Leydesdorff, Loet +2 more
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The role of the user and the society in new product development [PDF]
, 2010 Within the knowledge-based economy several institutions are involved in product innovation processes. Literature study has shown that the most researched and cited are the industry-universitygovernment relations, presented in the Triple Helix model of ...
Fain, Nusa, Duhovnik, Joze, Moes, Niels
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A triple product identity for Schur functions [PDF]
, 1991 In this paper we expand the product of n different classical theta functions into a Laurent sum of Schur symmetric functions of their arguments. This expansion is a natural extension of the Jacobi triple product identity.
Milne, S.C
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Advanced Functional Materials, EarlyView.HfxZr1−xO2${\rm Hf}_x{\rm Zr}_{1-x}{\rm O}_2$ offers CMOS‐compatible nanoscale ferroelectricity yet suffers from a high Ec${\rm E}_c$ demanding large operating voltages. A unified phase‐field framework spanning AFE/FE/DE phases shows how FE grains soften neighboring AFE grains over λ$\lambda$ ≈$\approx$ 22–37 nm.
P. Pankaj +4 more
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Triple product identities for the Jacobi symbol
Expositiones Mathematicae, 2001 Choose three \(2\times 2\) matrices \(A_j=\left(\begin{matrix} a_j & b_j\\ c_j & d_j\end{matrix}\right)\) with integer entries having \(c_j\) odd and positive such that \(A_1A_2A_3=-I\). The author shows that the product of the Jacobi symbols \(\prod^3_{j=1} \left(\frac{a_j}{c_j}\right)\) is \((-1)\) to the power \(\frac 14\sum_ ...
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