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In this paper, we continue the work of Jang et al. and classify the ( − 3 ) -saturated indecomposable fat Hoffman graphs with an integral representation of norm 3. This gives a contribution to Problem 4 of Woo and Neumaier. [ABSTRACT FROM AUTHOR]

A class of Stieltjes functions of finite type is introduced. These satisfy Widder’s conditions on the successive derivatives up to some finite order and are not necessarily smooth. We show that such functions have a unique integral representation along some generic kernel which is a truncated Laurent series approximating the standard Stieltjes kernel. We then obtain a two-to-one correspondence, via the logarithmic derivative, between these functions and a subclass of hyperbolically monotone functions of finite type. This correspondence generalizes a representation of HCM functions in terms of two Stieltjes transforms earlier obtained by the first author. [ABSTRACT FROM AUTHOR]

It is shown that every continuous valuation defined on n -dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly continuous on bounded sets. We also characterize continuous valuations on the n -dimensional star bodies that arise as restriction of a measure on R n . [ABSTRACT FROM AUTHOR]

In this paper our aim is to establish the Paley–Wiener Theorem for the Weinstein Transform. Furthermore, some applications are presents. In particular some properties for the generalized translation operator associated with the Weinstein operator are proved, an integral representation and a series representation for a function in the Paley–Wiener classes are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we study optimal estimates and comparison of the coefficients in the Gegenbauer series expansion. We propose aalternative derivation of the contour integral representation of the Gegenbauer expansion coefficients which was recently derived by Cantero and Iserles [SIAM J. Numer. Anal., 50 (2012), pp. 307--327]. With this representation, we show that optimal estimates for the Gegenbauer expansion coefficients can be derived, which in particular includes Legendre coefficients as a special case. Further, we apply these estimates to establish some rigorous and computable bounds for the truncated Gegenbauer series. In addition, we compare the decay rates of the Chebyshev and Legendre coefficients. For functions whose singularity is outside or at the endpoints of the expansion interval, asymptotic behavior of the ratio of the $n$th Legendre coefficient to the $n$th Chebyshev coefficient is given, which provides us an illuminating insight for the comparison of spectral methods based on Legendre and Chebyshev expansions. [ABSTRACT FROM AUTHOR]

By judicious exploitation of the transpose operator relation in conjunction with the differential equations of special functions of mathematical physics, integral representations of the on- and off-shell Jost functions are derived from the particular integrals of the inhomogeneous Schrödinger equation. Using the particular integral of the inhomogeneous Schrödinger equation, exact analytical expressions for the Coulomb and Coulomb plus Yamaguchi off-shell Jost solutions are constructed in the maximal reduced form. As a case study, the limiting behaviours and the on-shell discontinuities of the Coulomb plus Yamaguchi Jost solutions are verified numerically. [ABSTRACT FROM AUTHOR]

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then a series representation and asymptotics of the fundamental solution are discussed. The fundamental solution is interpreted as a probability density function and its entropy in the Shannon sense is calculated. The entropy production rate of the stochastic process governed by the α-fractional diffusion equation is shown to be equal to one of the conventional diffusion equation. [ABSTRACT FROM AUTHOR]

With methods of potential theory, we develop a representation of a solution of the coupled Stokes-Darcy model in a Lipschitz domain for boundary data in H-1/2. [ABSTRACT FROM AUTHOR]

Integral representations of series coefficients for components of an electromagnetic field with nuclei are formulated in the form of Green's functions. Approximate quasi-static analogs are used as these functions. An example of the translational motion of the sphere is presented. Explicit formulas for the components of the electromagnetic field are derived. [ABSTRACT FROM AUTHOR]

For a given algebraic number field F we consider a normal extension E/F of finite degree d and finite abelian subgroups G ⊂ GLn(E) of a given exponent t. We assume that G is stable under the natural action of the Galois group of E/F and consider fields E = F(G) that are obtained via adjoining all matrix coefficients of all matrices g ∊ G to F. It is proved that under some reasonable restrictions for n any E can be realized as F(G), while if all coefficients of matrices in G are algebraic integers, there are only finitely many fields E = F(G) for prescribed integers n and t or prescribed n and d. Some related results and conjectures are considered. [ABSTRACT FROM AUTHOR]

The article presents sample applications of integral representation theory of finite groups. It uses the finitely generated abelian groups and other equivalent finitely generated modules. It also evaluates the representations of the abstract group theory, algebraic topology, and algebraic number theory.

Using Carleman's formula of a harmonic function in the half space and Nevanlinna's representation of a harmonic function in the half sphere, we prove that a harmonic function, whose positive part satisfies a slowly growing condition, can be represented by a certain integral. This improves some classical Poisson integrals for harmonic functions. [ABSTRACT FROM AUTHOR]

Abstract: 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 results extend and generalize some known conclusions. [Copyright &y& Elsevier]

This paper deals with the study of the integral representations involving the product of the Aleph function with exponential function, Gauss hypergeometrc function and Fox's H-function. The results derived in this paper are basic in nature and include a number of known and new results as special cases. [ABSTRACT FROM AUTHOR]

Abstract: In the paper, the author establishes several integral representations and properties of Stirling numbers of the first kind. [Copyright &y& Elsevier]

We extend the technique of using the trapezoidal rule for efficient evaluation of the special functions of mathematical physics given by integral representations. This technique was recently used for Bessel functions, and here we treat incomplete gamma functions and the general confluent hypergeometric function. [ABSTRACT FROM AUTHOR]

A multidimensional generalization of the class of Bernstein functions is introduced and the properties of functions belonging to this class are studied. In particular, a new proof of the integral representation of Bernstein functions of several variables is given. Examples are considered. [ABSTRACT FROM AUTHOR]

We study the Dirichlet problem for the equation Δu - k2u = 0 in the exterior of nonclosed Lipschitz surfaces in R3. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable. [ABSTRACT FROM AUTHOR]

In this paper, we obtain all the symmetric semi-classical linear functionals of class three taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention on their integral representations. Thus, some linear functionals very well known in the literature, associated with perturbations of semi-classical linear functionals of class one at most, appear as well as new linear functionals which have not been studied. [ABSTRACT FROM PUBLISHER]

In this paper, we prove that if the positive part u+(x) of a harmonic function u(x) in the upper half space satisfies a fast growing condition, then its negative part u-(x) can also be dominated by a similar growing condition. Meanwhile, u(x) can be represented in terms of the modified Poisson integral and a harmonic function vanishing on the boundary. [ABSTRACT FROM AUTHOR]

Abstract: We prove an extension of the Ocone–Karatzas integral representation, valid for all functions on the classical Wiener space. We also establish an elementary chain rule formula and combine the two results to compute explicit integral representations for some classes of composite random variables. [Copyright &y& Elsevier]

Previously, we derive a representation of q-deformed $${\mathfrak{gl}_{\ell+1}}$$ -Whittaker function as a sum over Gelfand-Zetlin patterns. This representation provides an analog of the Shintani-Casselman-Shalika formula for q-deformed $${\mathfrak{gl}_{\ell+1}}$$ -Whittaker functions. In this note, we provide a derivation of the Givental integral representation of the classical $${\mathfrak{gl}_{\ell+1}}$$ -Whittaker function as a limit q → 1 of the sum over the Gelfand-Zetlin patterns representation of the q-deformed $${\mathfrak{gl}_{\ell+1}}$$ -Whittaker function. Thus, Givental representation provides an analog the Shintani-Casselman-Shalika formula for classical Whittaker functions. [ABSTRACT FROM AUTHOR]

We obtain an integral representation of even functions of two variables for which the kernel [ k( x + y) + k( x − y)], x, y ∈ R, is positive definite. [ABSTRACT FROM AUTHOR]

Let F be a finite extension of ℚ. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over $\overline{ \mathbb{F}}_{p}$ to be supersingular. We then give the classification of irreducible admissible smooth GL( F)-representations over $\overline{ \mathbb{F}}_{p}$ in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel-Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present various integral representations for the Chan–Chyan–Srivastava, Lagrange–Hermite, Erkus–Srivastava multivariable polynomials and extended Jacobi polynomials. Then, we obtain some partial differential equations for the product of any two of them. We show that the Chan–Chyan–Srivastava multivariable polynomials are not orthogonal. We also discuss other miscellaneous properties of the Chan–Chyan–Srivastava, Lagrange–Hermite and Erkus–Srivastava multivariable polynomials. [Copyright &y& Elsevier]

Abstract: The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials and the generalized Cesàro polynomials. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. [Copyright &y& Elsevier]

The real-valued Lambert W-functions considered here are w( y) and w( y), solutions of we = y, − 1/ e < y < 0, with values respectively in ( − 1,0) and ( − ∞ , − 1). A study is made of the numerical evaluation to high precision of these functions and of the integrals $\int_1^\infty [-w_0(-xe^{-x})]^\alpha x^{-\beta}\d x$, α > 0, β ∈ ℝ, and $\int_0^1 [-w_{-1}(-x e^{-x})]^\alpha x^{-\beta}\d x$, α > − 1, β < 1. For the latter we use known integral representations and their evaluation by nonstandard Gaussian quadrature, if α ≠ β, and explicit formulae involving the trigamma function, if α = β. [ABSTRACT FROM AUTHOR]

A (2+1)-dimensional rotating shallow water system with an underlying circular paraboloidal bottom topography is shown to admit a multiparameter integrable nonlinear subsystem of Ermakov-Ray-Reid type. The latter system, which describes the time evolution of the semi-axes of the elliptical moving shoreline on the paraboidal basin, is also Hamiltonian. The complete solution of the generic eight-dimensional dynamical system governing the reduction is obtained in terms of an elliptic integral representation. [ABSTRACT FROM AUTHOR]

We obtain an integral representation of even positive-definite functions of one variable for which the kernel [ k( x + y) + k ( x − y)] is positive definite. [ABSTRACT FROM AUTHOR]

Since the time of Euler, the so-called Euler-Mascheroni constant γ has been involved in a wide variety of important mathematical formulas and results. Among these formulas and results, a considerably large number of integral representations of γ have been developed. Here we aim at investigating several further integral expressions for the Euler-Mascheroni constant γ. [ABSTRACT FROM AUTHOR]

The field scattered by a plane composed of several homogenous layers on a perfectly reflecting plane is generally given by its plane wave expansion (Fourier representation). We here develop another approach to express the field, more suitable for point source illumination. For this, we sum the contributions of modes corresponding to zeros gj (or poles – gj) of the reflection coefficient of the imperfectly reflecting surface, developing an original integral representation and its expansions, valid for arbitrary mode which can be passive or active. Particular attention has been paid to active modes with Regj < 0, and to the vicinity of the mode with gj = – 1. We then obtain novel exact expressions for the field in acoustics and for potentials in electromagnetism. [ABSTRACT FROM PUBLISHER]

In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks’ integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature. [ABSTRACT FROM AUTHOR]

We study the Dirichlet problem for the static elasticity equations outside several curvilinear cracks on the plane. The existence and uniqueness of a classical solution are proved. We obtain an integral representation of the solution in the form of potentials whose densities are determined from a uniquely solvable system of Fredholm integral equations of the second kind. We analyze the singularities of the derivatives of the solution at the endpoints of open curves and obtain a closed-form solution of the problem for the case in which all cracks are located along segments of one and the same straight line. [ABSTRACT FROM AUTHOR]

Let K/ℚ be a finite Galois extension with maximal order $\mathcal{O}_K$ and Galois group Γ. For finite Γ-stable subgroups $G \subset GL_n (\mathcal{O}_K)$ it is known [4], that they are generated by matrices with coefficients in $\mathcal{O}_{K_{ab}}$, Kab the maximal abelian subextension of K over ℚ. This note gives a contribution to the corresponding question in the case of a relative Galois extension K/R, where R is a finite extension of the rationals ℚ. It turns out, that in this relative situation the answer to the corresponding question depends heavily on the arithmetic of the number field R, more precisely on the ramification behavior of primes in K/R. Due to the possibility of unramified extensions of R for certain number fields R there exist examples of Galois stable linear groups $G \subset GL_n (\mathcal{O}_K)$ which are not fixed elementwise by the commutator subgroup of Gal(K/R). [ABSTRACT FROM AUTHOR]

We investigate the integral representation of infinite sums involving the reciprocals of double binomial coefficients. We also recover some well-known representations of ζ (2) and other related identities. [ABSTRACT FROM AUTHOR]

In this study, we shall suggest analytical expressions for two-center nuclear attraction integrals over STO’s with a one-center charge distribution by using Fourier transform method. The derivation is based on partial-fraction decompositions and Taylor expansions of rational functions. Analytical expressions obtained by this method are expressed in terms of Gegenbauer, and binomial coefficients and linear combinations of STO’s. Finally, it is relatively easy to express the Fourier integral representations of two-center nuclear attraction integrals with a one-center charge distribution mentioned above as finite and infinite of series of STO’s and irregular solid harmonics which may be considered to be limiting cases of STO’s. [ABSTRACT FROM AUTHOR]

We investigate the integral representation of infinite sums involving the ratio of binomial coefficients. We also recover some well-known properties of ζ (3) and extend the range of results given by other authors. [ABSTRACT FROM AUTHOR]

In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers. [ABSTRACT FROM AUTHOR]

We obtain integral representations of generalized axially symmetric potentials via analytic functions of a complex variable that are defined in an arbitrary simply connected bounded domain symmetric with respect to the real axis. We prove that these integral representations establish a one-to-one correspondence between analytic functions of a complex variable that take real values on the real axis and generalized axially symmetric potentials of certain classes. [ABSTRACT FROM AUTHOR]

A numerical algorithm for calculating the generalized Mittag-Leffler Eα,≈(z) function for arbitrary complex argument z and real parameters α > 0 and β ϵ ℝ is presented. The algorithm uses the Taylor series, the exponentially improved asymptotic series, and integral representations to obtain optimal stability and accuracy of the algorithm. Special care is applied to the limits of validity of the different schemes to avoid instabilities in the algorithm. [ABSTRACT FROM AUTHOR]

Abstract.  We derive a functional integral representation for the partition function of a many Boson system for which the configuration space consists of finitely many points. [ABSTRACT FROM AUTHOR]

By using some recently investigated Fourier sine integral representations for the Mathieu type series (see [4]), new integral and series representations are derived here for certain general families of Mathieu type series. [ABSTRACT FROM AUTHOR]

We study linear and quasi-linear elliptic equations containing the Bessel operator with respect to a selected variable (so-called special variable). The well-posedness of the nonclassical Dirichlet problem (with the additional condition of evenness with respect to the special variable) in the half-space is proved, an integral representation of the solution is constructed, and a necessary and sufficient condition of stabilization is established. The stabilization is understood as follows: the solution has a finite limit as the independent variable tends to infinity along the direction orthogonal to the boundary hyperplane. [ABSTRACT FROM AUTHOR]

Simple formulae of similar type for the number of quadrics and symmetric forms of modules over local rings are found analytically. This simplification of known formulae of Levchuk and Starikova is achieved using integral representation method of combinatorial summation and leads to number-theoretical identities of new type. The problem of algebraic interpretation of new formulae is posed. [ABSTRACT FROM AUTHOR]

An explicit integral representation by single definite integrals of the fundamental matrix (Green's tensor) of the time-dependent system of hexagonal elastic media is derived. Thereby the problem of internal conical refraction in such media is solved. [ABSTRACT FROM PUBLISHER]

Abstract: In this article, we study the semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient in the linear parabolic equation , with Dirichlet boundary conditions , . Main goal of this study is to investigate the distinguishability of the input–output mappings , via semigroup theory. In this paper, we show that if the null space of the semigroup consists of only zero function, then the input–output mappings and have the distinguishability property. Moreover, the values and of the unknown diffusion coefficient at and , respectively, can be determined explicitly by making use of measured output data (boundary observations) or/and . In addition to these, the values and of the unknown coefficient at and , respectively, are also determined via the input data. Furthermore, it is shown that measured output data and can be determined analytically, by an integral representation. Hence the input–output mappings , are given explicitly in terms of the semigroup. Finally by using all these results, we construct the local representations of the unknown coefficient at the end points and . [Copyright &y& Elsevier]