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Ukrainian Mathematical Journal

, Volume 60, Issue 7, pp 1055–1072 | Cite as

Solution of a second-order Poincaré-Perron-type equation and differential equations that can be reduced to it

  • V. E. Kruglov
Article

We give an analytic solution of a second-order difference Poincaré-Perron-type equation. This enables us to construct a solution of the differential equation {fx1055-01} in explicit form. A solution of this equation is expressed in terms of two hypergeometric functions and one new special function. As a separate case, we obtain an explicit solution of the Heun equation and determine its polynomial solutions.

Keywords

Power Series Hypergeometric Function Explicit Solution Maximum Order Polynomial Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • V. E. Kruglov
    • 1
  1. 1.Volyn National UniversityLuts’kUkraine

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