Related papers: Differential Equations, Associators, and Recurrenc…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
We develop the method of the hamiltonian reduction of affine Lie superalgebras to obtain explicit and general expressions both for the classical and the quantum extended superconformal algebras. By performing the gauge transformation which…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].…
We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…
A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the…
It is shown that the expansion methods developed in refs. arXiv:hep-th/0212347 and arXiv:hep-th/0401033v2 can be generalized so that they permit to study the expansion of algebras of loops, both when the compact finite-dimensional algebra…
Physically relevant field-theoretic quantities are usually derived from perturbation techniques. These quantities are solved in the form of an asymptotic series in powers of small perturbation parameters related to the physical system, and…
In this paper, using similar symbolical method of Burchnall and Chaundy formulas of expansion for the generalized hypergeometric function were constructed. By means of the found formulas of expansion the formulas of an analytic continuation…
Mathematical structure of the reflection coefficients for the one-dimensional Fokker-Planck equation is studied. A new formalism using differential operators is introduced and applied to the analysis in high- and low-energy regions.…
We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
We present a novel framework for computing differential cross-sections in quantum field theory using the optical theorem and loop amplitudes, circumventing the traditional method of squaring scattering amplitudes. This approach addresses…
A new formalism is presented for high-energy analysis of the Green function for Fokker-Planck and Schr\"odinger equations in one dimension. Formulas for the asymptotic expansion in powers of the inverse wave number are derived, and…
We review our recent formulation of Colombeau type algebras as Hausdorff sequence spaces with ultranorms, defined by sequences of exponential weights. We extend previous results and give new perspectives related to echelon type spaces,…
Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for…
We prove hypercontractive inequalities on high dimensional expanders. As in the settings of the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities are effective for global functions, which are functions that…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…