@**inproceedings**{RISC4582,author = {Moulay A. Barkatou and Clemens G. Raab},

title = {{Solving Linear Ordinary Differential Systems in Hyperexponential Extensions}},

booktitle = {{Proceedings of ISSAC 2012}},

language = {english},

abstract = {Let F be a differential field generated from the rational functions over some constant field by one hyperexponential extension. We present an algorithm to compute the solutions in F^n of systems of n first-order linear ODEs. Solutions in F of a scalar ODE of higher order can be determined by an algorithm of Bronstein and Fredet. Our approach avoids reduction to the scalar case. We also give examples to show how this can be applied to integration.},

pages = {51--58},

isbn_issn = {ISBN 978-1-4503-1269},

year = {2012},

editor = {Joris van der Hoeven and Mark van Hoeij},

refereed = {yes},

keywords = {Linear Differential Equations over hyperexponential extension, Closed form solutions, Computer Algebra},

sponsor = {Austrian Science Fund (FWF)},

length = {8},

conferencename = {37th International Symposium on Symbolic and Algebraic Computation, ISSAC 2012}

}