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

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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.

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Author information

Correspondence to V. E. Kruglov.

Additional information

Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 900–917, July, 2008.

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Kruglov, V.E. Solution of a second-order Poincaré-Perron-type equation and differential equations that can be reduced to it. Ukr Math J 60, 1055–1072 (2008). https://doi.org/10.1007/s11253-008-0120-x

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Keywords

  • Power Series
  • Hypergeometric Function
  • Explicit Solution
  • Maximum Order
  • Polynomial Solution