Related papers: A family of polylogarithmic integrals
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
We extend the (continuous) multivariate Almkvist-Zeilberger algorithm in order to apply it for instance to special Feynman integrals emerging in renormalizable Quantum field Theories. We will consider multidimensional integrals over…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
Beginning with Hermite's integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type $\int_0^\infty…
We show that solutions of the Schr\"odinger equation with a symmetric P\"oschl-Teller potential of a particular form can be expressed in terms of a closed combination (not series) of trigonometric functions. Using some properties of the…
This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
The general analytical expressions for the thermal radiative and thermodynamic properties of a real-body are obtained in a finite range of frequencies at different temperatures. The frequency dependence of the spectral emissivity is…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
We derive new Poincar\'e-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus…
Many signals in Nature, technology and experiment have a multi-component structure. By spectral decomposition and projection on the eigenvectors of a family of unitary operators, a robust method is developed to decompose a signals in its…
In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short $S$-sums) arise. They are characterized by…
This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…
We present the details of a recently discovered representation of conformal four-point ladder integrals as thermal one-point functions in scalar field theories. We show that the conformal ladder integrals can be constructed from the…
The integral representation of the Hadamard product of two functions is used to prove several Euler-type series transformation formulas. As applications we obtain three binomial identities involving harmonic numbers and an identity for the…
A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A…
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…
The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the…