Related papers: Connection formulas for the lambda generalized Isi…
In this paper, we obtained some global approximation results for general Gamma type operators.
Using the variational formula for operator product coefficients a method for perturbative calculation of the short-distance expansion of the Spin-Spin correlation function in the two dimensional Ising model is presented. Results of explicit…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
We calculate the local Fourier transforms for formal connections. In particular, we verify an analogous conjecture suggested in Laumon's paper: "Transformation de Fourier, constantes d'equations fonctionnelles et conjecture de Weil, 2.6.3".
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
We derive a Toda-type recurrence relation, in both high and low temperature regimes, for the $\lambda$ - extended diagonal correlation functions $C(N,N;\lambda)$ of the two-dimensional Ising model, using an earlier connection between…
The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
In this paper we derive some asymptotic formulas for the $q$-Gamma function $\Gamma_{q}(z)$ for $q$ tending to 1.
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…
In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some…
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…
The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…
For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These…
We present a systematic prescription for calculating cosmological correlation functions for models with derivative interactions through the wavefunction of the universe and compare this result with the "in-in" formalism -- canonical…