• Corpus ID: 207780605

On the Form of Solutions of Fuchsian differential Equations with n regular singular Points

@article{Huber2019OnTF,
  title={On the Form of Solutions of Fuchsian differential Equations with n regular singular Points},
  author={Albert Huber},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
  • A. Huber
  • Published 4 November 2019
  • Mathematics
  • arXiv: Mathematical Physics
The form of the coefficients of power series expressions corresponding to solutions of Fuchsian differential equations (or their associated degenerated confluent forms) with n regular singular points is determined by solving the corresponding n-term recurrence relations in full generality. Some important special cases are discussed in which the solutions coincide with special functions of mathematical physics. 
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The gravitational field of a massless particle on the horizon of a stationary black hole

  • A. Huber
  • Physics
    Classical and Quantum Gravity
  • 2019
In this work, the field of a gravitational shockwave generated by a massless point-like particle is calculated at the event horizon of a stationary Kerr–Newman black hole. Using the geometric…

References

SHOWING 1-10 OF 37 REFERENCES

Solutions of Linear Difference Equations with Variable Coefficients

The explicit solution of a linear difference equation of unbounded order with variable coefficients is presented. As special cases, the solutions of nonhomogeneous and homogeneous linear difference…

Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. As a new example we find that while the Dirac equation written in the background…

Special Functions: A Unified Theory Based on Singularities

Preface 1. Linear Second-order ODE with Polynomial Coefficients 2. The Hypergeometric Class of Equations 3. The Heun Class of Equations 4. Application to Physical Sciences 5. The Painleve Class of…

Exact solutions of Regge-Wheeler equation

The Regge-Wheeler equation describes the axial perturbations of Schwarzschild metric in linear approximation. We present its exact solutions in terms of the confluent Heun's functions, the basic…

Expansions in Products of Heine—Stieltjes Polynomials

Abstract. It is shown that products of polynomials introduced by Heine and Stieltjes form orthogonal bases in suitable function spaces. A theorem on the expansion of analytic function in these bases…

A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions

We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrodinger equation is written through the first derivative of a…

Classes of exact solutions to the Teukolsky master equation

The Teukolsky master equation is the basic tool for the study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky radial…

The generalized Heun equation in QFT in curved spacetimes

In this paper we give a brief outline of the applications of the generalized Heun equation (GHE) in the context of quantum field theory in curved spacetimes. In particular, we relate the separated…

Complex Cobordism and Stable Homotopy Groups of Spheres

An introduction to the homotopy groups of spheres Setting up the Adams spectral sequence The classical Adams spectral sequence $BP$-theory and the Adams-Novikov spectral sequence The chromatic…

Heun Functions and their uses in Physics

Most of the theoretical physics known today is described using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric…