Numerical Algorithms

, Volume 71, Issue 4, pp 797–809 | Cite as

Global solutions of the biconfluent Heun equation

  • E. M. Ferreira
  • J. Sesma
Original Paper


An algorithm is proposed for obtaining global solutions of the biconfluent Heun equation, which appears when dealing with a variety of physical problems. The procedure, which provides algebraic expressions of the solutions in the form of convergent series or asymptotic expansions, lies on the determination of the connection factors relating the solutions about the regular singular point at the origin and the irregular one at infinity. The algorithm is illustrated by examples.


Differential equations Biconfluent Heun equation Connection factors Eigenvalues 

Mathematics Subject Classification (2010)

34B30 33E20 34M40 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal do Rio de JaneiroRio de JaneiroBrasil
  2. 2.Departamento de Física TeóricaFacultad de CienciasZaragozaSpain

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