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

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.


Power Series Hypergeometric Function Explicit Solution Maximum Order Polynomial Solution 
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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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