Related papers: Integral Representations for Computing Real Parabo…
We describe the utility of integral representations for sums of basic hypergeometric functions. In particular we use these to derive an infinite sequence of transformations for symmetrizations over certain variables which the functions…
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…
For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for…
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…
Series involving hypergeometric functions are used to derive, extend and evaluate integrals involving the product of two Bessel functions of the first kind $J_{u}(a z)$ $J_{v}(b z)$ with order $u,v$, studied by Landau et al. The method used…
This paper extends the parabolic integral equation method, which is very effective for forward scattering from rough surfaces, to include backscatter. This is done by applying left-right splitting to a modified two-way governing integral…
In this article, we present the integral representations of the power series diagonals. Such representations are obtained by lowering the integration multiplicity for the previously known integral representation. The procedure is carried…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
In this paper, the product of parabolic cylinder functions $D_{\nu}(\pm z)D_{\nu+\mu-1}(z)$, with different parameters $\mu$ and $\nu$, are established in terms of Laplace and Fourier transforms of Kummer's confluent hypergeometric…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
Linear second-order ordinary differential equations of the form $d^{2}w/dz^{2}=\{u^{2}f(a,z)$ $+g(z)\}w$ are studied for large values of the real parameter $u$, where $z$ ranges over a bounded or unbounded complex domain $Z$, and $a_{0} \le…
A system of commutative complex numbers in 5 dimensions of the form u=x_0+h_1x_1+h_2x_2+h_3x_3+h_4x_4 is described in this paper, the variables x_0, x_1, x_2, x_3, x_4 being real numbers. The operations of addition and multiplication of the…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we…
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…
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…