相关论文: Integral Representations of the Macdonald Symmetri…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such functions by using elementary methods. Especially, we obtain…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.
In this paper we give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities involving $r$-Stirling numbers, $r$-Whitney numbers and…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
Inhomogeneous analogues of symmetric and nonsymmetric Macdonald polynomials were introduced by F. Knop and the author. In the symmetric case A. Okounkov has recently proved a beautiful expansion formula which can be viewed as a…
Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
For any homomorphism V on the space of symmetric functions, we introduce an operation which creates a q-analog of V. By giving several examples we demonstrate that this quantization occurs naturally within the theory of symmetric functions.…
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…
We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1) \times SO(q)$. We…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
We follow the general recipe for constructing commutative families of $W$-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to…