Integral representation of a solution of Heun's general equation

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dc.contributor.authorBatola, Francois
dc.contributor.authorBatola, Jomo
dc.date.accessioned2021-08-13T15:32:19Z
dc.date.available2021-08-13T15:32:19Z
dc.date.issued2007-06-21
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBatola, F., & Batola, J. (2007). Integral representation of a solution of Heun's general equation. Electronic Journal of Differential Equations, 2007(94), pp. 1-11.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14310
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectHeun equation
dc.subjectHeun function
dc.subjectIntegral representation
dc.subjectAnalytic continuation
dc.subjectExtension of Mellin lemma
dc.subjectIntegral relation
dc.titleIntegral representation of a solution of Heun's general equation
dc.typeArticle

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