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Representations of the celebrated Heisenberg commutation relations in quantum mechanics (and their exponentiated versions) form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we will try to bridge the two communit...

In this paper, the author establishes a set of three new theta-function identities involving Rα, Rβ and Rm functions which are based upon number q-product Jacobi’s celebrated triple-product identity. These depict inter-relationships that exist among combinatorial partition-theoretic identities. Here, in paper we answer open question Srivastava et al [33], established relations terms (for m = 1,...

‎The problem of shrinkage testimation (test-estimation) for the Rayleigh scale‎ ‎parameter θ based on censored samples under the reflected‎ ‎gamma loss function is considered‎. We obtain the minimum risk‎ ‎estimator among a subclass and compute its risk‎. ‎A shrinkage‎ ‎testimator based on acceptance or rejection of a null hypothesis&lr...

The Abelian current algebra on the lattice is given from a series of the independent Weyl pairs and the shift operator is constructed by this algebra. So the realization of the operators of the braid group is obtained. For |q| = 1 the shift operator is the product of the theta functions of the generators w n of the current algebra. For |q| = 1 it can be expressed by the quantum dilogarithm of w...

The main goal of this paper is to give a modular type representation for the infinite product (1−x)(1−xq)(1−xq)(1−xq) · · · . It is shown that this representation essentially contains the well-known modular formulae either for Dedekind’s eta function, Jacobi theta function or for certain Lambert series. Thus a new and unified approach is outlined for the study of elliptic and modular functions ...