dc.contributor.author Batola, Francois ( ) dc.contributor.author Batola, Jomo ( ) dc.date.accessioned 2021-08-13T15:32:19Z dc.date.available 2021-08-13T15:32:19Z dc.date.issued 2007-06-21 dc.identifier.citation Batola, F., & Batola, J. (2007). Integral representation of a solution of Heun's general equation. Electronic Journal of Differential Equations, 2007(94), pp. 1-11. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/14310 dc.description.abstract We establish an integral representation for the Frobenius solution with an exponent zero at z = 0 of the general Heun equation. First we present an extension of Mellin's lemma which provides a powerful method that takes into account differential equations which are not of the form studied by Mellin. That is the case for equations of Heun's type. It is that aspect which makes our work different from Valent's work. The method is powerful because it allows obtaining directly the nucleus equation of the representation. The integral representation formula obtained with this method leads quickly and naturally to already known results in the case of hypergeometric functions. The generalisation of this method gives a type of differential equations which form is a novelty and deserves to be studied further. en_US dc.format Text dc.format.extent 11 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University-San Marcos, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Heun equation en_US dc.subject Heun function en_US dc.subject Integral representation en_US dc.subject Analytic continuation en_US dc.subject Extension of Mellin lemma en_US dc.subject Integral relation en_US dc.title Integral representation of a solution of Heun's general equation en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
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