Solution of Differential Equations in Terms of Gauss Hypergeometric Functions

ABSTRACT We consider second‐order linear differential equations with coefficients in . In this paper, we investigate the existence of solutions expressible in terms of the Gauss hypergeometric function, specifically of the form where , and . We further assume that the function field is a subfield of of index 2 or 3, or that is a Möbius transformation of a monomial, that is, for some positive integer and constants .

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Publication Details

Journal
Mathematical Methods in the Applied Sciences
Published
2025-12-12
DOI
https://doi.org/10.1002/mma.70413
Primary Topic
Polynomial and algebraic computation
Type
article
Field-Weighted Citation Impact
0.00

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article

Solution of Differential Equations in Terms of Gauss Hypergeometric Functions

Mathematical Methods in the Applied Sciences
Polynomial and algebraic computation
article

Solution of Differential Equations in Terms of Gauss Hypergeometric Functions

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Abstract

ABSTRACT We consider second‐order linear differential equations with coefficients in . In this paper, we investigate the existence of solutions expressible in terms of the Gauss hypergeometric function, specifically of the form where , and . We further assume that the function field is a subfield of of index 2 or 3, or that is a Möbius transformation of a monomial, that is, for some positive integer and constants .

Mathematical Methods in the Applied Sciences
King Saud University (SA)
King Saud University
Openalex Percentile: Top 30%
Polynomial and algebraic computation
DOIOpen Access PDFOpenAlex
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Solution of Differential Equations in Terms of Gauss Hypergeometric Functions · Mathematical Methods in the Applied Sciences (2025) | TGRS Research Map | TGRS