Abstract
The multivariable Euler transform of a solution of the system of linear ordinary differential equations of Okubo normal form is considered. The Pfaffian system satisfied by the transform is derived. Applications to the Appell hypergeometric functions \(F_{1}\), \(F_{3}\), and the Lauricella hypergeometric function \(F_{D}\) are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dettweiler, M., Reiter, S.: An algorithm of Katz and its application to the inverse Galois problem. J. Symb. Comput. 30, 761–798 (2000)
Golubeva, V.A.: Appell-Kampé de Fériet hypergeometric functions of two variables. Sib. Math. J. 20, 705–717 (1979)
Katz, N.M.: Rigid Local Systems. Annals of Mathematics Studies. Princeton University Press, Princeton (1996)
Leksin, V.P.: Multidimensional Jordan-Pochhammer systems and their applications. Proc. Steklov Inst. Math. 278, 130–138 (2012)
Okubo, K.: Connection problems for systems of linear differential equations. In: Japan-United States Seminar on Ordinary Differential and Functional Equations. Lecture Notes in Mathematics, pp. 238–248. Springer, Berlin (1971)
Schlesinger, L.: Einführung in die Theorie der gewöhnlichen Differentialgleichungen auf funktionentheoretischer Grundlage. Walter de Gruyter & Co., Berlin (1922)
Yokoyama, T.: Recursive calculation of connection formulas for systems of differential equations of Okubo normal form. J. Dyn. Control Syst. 20, 241–292 (2014)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yokoyama, T. Multivariable Euler transform of systems of linear ordinary differential equations of Okubo normal form. Ramanujan J 42, 157–172 (2017). https://doi.org/10.1007/s11139-015-9753-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11139-015-9753-1