New indefinite integrals of Heun functions

D. Batic, O. Forrest, M. Nowakowski

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also derive new indefinite integrals involving the Gauss hypergeometric function and products of hypergeometric functions with elliptic functions of the first kind. All integrals we obtained cannot be computed using Maple and Mathematica.

Original languageBritish English
Pages (from-to)794-804
Number of pages11
JournalIntegral Transforms and Special Functions
Issue number10
StatePublished - 3 Oct 2018


  • 33C05
  • 33C55
  • 33E05
  • 33E99
  • 34A99
  • 70H03
  • complete elliptic integrals
  • Heun functions
  • hypergeometric functions
  • Special functions


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