Results 121 to 130 of about 3,610,072 (153)

Polysorbates degrading enzymes in biotherapeutics - a current status and future perspectives. [PDF]

Front Bioeng Biotechnol
Felix MN, Waerner T, Lakatos D, Reisinger B, Fischer S, Garidel P.   +5 more
europepmc   +1 more source

Educational cooperation in the perspective of tripartite evolutionary game among government, enterprises and universities. [PDF]

PLoS One
Zhang S.
europepmc   +1 more source

Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime. [PDF]

Stoch Partial Differ Equ
Gasteratos I, Salins M, Spiliopoulos K.
europepmc   +1 more source

Gaussian sums, Dedekind sums and the Jacobi triple product identity

Gaussian sums, Dedekind sums and the Jacobi triple product identity
openaire   +1 more source

Euler's Pentagonal Number Theorem Implies the Jacobi Triple Product Identity

Integers, 2011
AbstractBy means of Liouville's theorem, we show that Euler's pentagonal number theorem implies the Jacobi triple product identity.
Chuanan Wei, Dianxuan Gong
exaly   +5 more sources

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Two generalizations of Jacobi’s triple product identity and their applications

Ramanujan Journal, 2022
There are two main theorems in the paper under review and they are exactly two generalizations of Jacobi's triple product identity. The proofs are based on the Andrews' series rearrangement method. As applications, the authors use their formulae for mock theta functions and Rogers-Ramanujan identities.
Qiuxia Hu, Chuanan Wei, Wei Chuanan
exaly   +2 more sources

Jacobi’s Triple-Product Identity and an Associated Family of Theta-Function Identities

Mathematical Notes, 2022
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 ...
Hari M Srivastava, M P Chaudhary, Srivastava H M   +2 more
exaly   +2 more sources

A combinatorial proof of Jacobi’s triple product identity

Ramanujan Journal, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Louis Kolitsch
exaly   +3 more sources

Jacobi’s Triple Product Identity

Universitext, 2002
We recall that the two Euler identities, (9.3) and (9.4), relate infinite products and infinite sums. In this chapter, we will use them to prove an important identity first discovered by Jacobi. Several interesting appli-cations of this identity in number theory will be explored in subsequent chapters.
Pokman Cheung, Kac VÍCTOR, Cheung Pokman   +2 more
exaly   +2 more sources