Aleksandrov, A. G.; Kuznetsov, A. N. Regular singular holonomic systems of differential equations with given integrals. (English) Zbl 1118.35016 J. Appl. Funct. Anal. 2, No. 1, 21-56 (2007). Summary: We develop an approach to the study of holonomic systems of differential equations with regular singularities along hypersurfaces. In particular, we investigate Picard-Fuchs systems satisfied by the elliptic, hyperelliptic and versal integrals, describe the corresponding minimal equations and analyze properties of their solutions. Cited in 1 Review MSC: 35N10 Overdetermined systems of PDEs with variable coefficients 35F05 Linear first-order PDEs 32S30 Deformations of complex singularities; vanishing cycles 32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects) 35A20 Analyticity in context of PDEs Keywords:versal integrals; hypergeometric functions; Gauss-Legendre equation; Picard-Fuchs systems PDFBibTeX XMLCite \textit{A. G. Aleksandrov} and \textit{A. N. Kuznetsov}, J. Appl. Funct. Anal. 2, No. 1, 21--56 (2007; Zbl 1118.35016)