Physical problems admitting Heun-to-hypergeometric reduction

@article{Aydiner2015PhysicalPA,
  title={Physical problems admitting Heun-to-hypergeometric reduction},
  author={Pelin Aydiner and Tolga Birkandan},
  journal={2015 Days on Diffraction (DD)},
  year={2015},
  pages={1-6}
}
The Heun's equation and its confluent forms emerge in many physical applications. However, the literature related to the mathematical analysis of the Heun's equation is far from complete in comparison with the hypergeometric equation which is known in detail. As a result, studying the reduction methods from Heun to hypergeometric equation is substantial for understanding the physical system better. In this work, Maier's Heun-to-hypergeometric reduction cases are studied for several physical… 
Heun Functions and Some of Their Applications in Physics
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  • 2018
Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric

References

SHOWING 1-10 OF 28 REFERENCES
On reducing the Heun equation to the hypergeometric equation
Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
We study Heun's differential equation in the case that one of the singularities is apparent. In particular, we propose a conjecture that solutions of Heun?s equation in this case also satisfy a
Parametric Transformations between the Heun and Gauss Hypergeometric Functions
The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with
NEW HYPERGEOMETRIC SERIES SOLUTIONS TO THE GENERAL HEUN EQUATION
We introduce new hypergeometric series expansions of the solutions to the general Heun equation. The form of the Gauss hypergeometric functions used as expansion function differs from that used
New solutions of Heun general equation
We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this property, we use the
Hypergeometric expansions of the solutions of the general Heun equation governed by two-term recurrence relations for expansion coefficients
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions the forms of which differ from
The 192 solutions of the Heun equation
TLDR
Of the 192 local solutions of the Heun equation, 24 are equivalent expressions for the local Heun function Hl, and it is shown that the resulting order-24 group of transformations of Hl is isomorphic to the symmetric group S 4 .
Heun's differential equations
A. HEUN'S EQUATION I: GENERAL AND POWER SERIES II: HYPERGEOMETRIC FUNCTION SERIES B. CONFLUENT HEUN EQUATION C. DOUBLE CONFLUENT HEUN EQUATION D. BICONFLUENT HEUN EQUATION E. TRICONFLUENT HEUN
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