相关论文: Infinite Product Representations fot Multiple Gamm…
We establish a derivative formula of $p$-adic Shintani $L$-functions, thus those of totally real $p$-adic Hecke $L$-functions with trivial moduli. As an application, we present a product formula of bivariate $p$-adic Gamma values by…
We construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent…
In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.
We provide an explicit description of the quantum product of multi-symmetric functions using the elementary multi-symmetric functions introduced by Vaccarino.
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
The Hermitian, complex and fermionic two-matrix models with infinite set of variables are constructed. We show that these two-matrix models can be realized by the $W$-representations. In terms of the $W$-representations, we derive the…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
For any discrete group $\Gamma$ and any 2-dimensional complex representation $\rho$ of $\Gamma$, we introduce the notion of $\rho-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also…
We derive a product formula for the multiple stochastic integrals with respect to Levy process. The idea is to use exponential vectors and the polarization technique which greatly simplify the argument.
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function $G(z;\tau)$. Second, we derive an algorithm for numerically…
We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of…
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…
We represent the volume product for the unit p-ball in a a form free of its gamma symbolism;this will enable us to confirm Mahler's lower bound and Santalo's upper bound by the use of basic only gamma function theory and moderately advanced…
It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz-Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life…
The Digamma and Polygamma functions are important tools in mathematical physics, not only for its many properties but also for the applications in statistical mechanics and stellar evolution. In many textbooks is found its develop almost by…
We obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values. Then we apply the formulas to prove several stuffle product formulas with one or two strings of $z_p$'s. We also describe how to…
We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.