@article{VANDERHOEVEN2007771,
    Abstract = {Let Θ=C[e−x1,{\ldots},e−xn][∂1,{\ldots},∂n] and S=C[x1,{\ldots},xn][[eCx1+⋯+Cxn]], where C is an effective field and x1N⋯xnNeCx1+⋯+Cxn and S are given a suitable asymptotic ordering ≼. Consider the mapping L:S→Sl;f↦(L1f,{\ldots},Llf), where L1,{\ldots},Ll∈Θ. For g=(g1,{\ldots},gl)∈SLl=imL, it is natural to ask how to solve the system Lf=g. In this paper, we will effectively characterize SLl and show how to compute a so called distinguished right inverse L−1:SLl→S of L. We will also characterize the solution space of the homogeneous equation Lh=0.},
    Author = {{van der Hoeven}, Joris},
    File = {Generalized power series solutions to linear partial differential equations - 1-s2.0-S0747717107000442-main - a.pdf},
    ISSN = {0747-7171},
    Journal = {Journal of Symbolic Computation},
    Keywords = {Linear partial differential equation, Asymptotics, Algorithm, Differential algebra, Formal power series, Tangent cone algorithm},
    Number = {8},
    Pages = {771-791},
    Title = {Generalized power series solutions to linear partial differential equations},
    URL = {https://www.sciencedirect.com/science/article/pii/S0747717107000442},
    Volume = {42},
    Year = {2007},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717107000442},
    bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2007.04.001},
    date-added = {2023-02-02 19:51:14 +0100},
    date-modified = {2023-02-02 19:51:14 +0100},
    doi = {10.1016/j.jsc.2007.04.001}
}

@article{VANDERHOEVEN2007771, Abstract = {Let Θ=C[e−x1,{\ldots},e−xn][∂1,{\ldots},∂n] and S=C[x1,{\ldots},xn][[eCx1+⋯+Cxn]], where C is an effective field and x1N⋯xnNeCx1+⋯+Cxn and S are given a suitable asymptotic ordering ≼. Consider the mapping L:S→Sl;f↦(L1f,{\ldots},Llf), where L1,{\ldots},Ll∈Θ. For g=(g1,{\ldots},gl)∈SLl=imL, it is natural to ask how to solve the system Lf=g. In this paper, we will effectively characterize SLl and show how to compute a so called distinguished right inverse L−1:SLl→S of L. We will also characterize the solution space of the homogeneous equation Lh=0.}, Author = {{van der Hoeven}, Joris}, File = {Generalized power series solutions to linear partial differential equations - 1-s2.0-S0747717107000442-main - a.pdf}, ISSN = {0747-7171}, Journal = {Journal of Symbolic Computation}, Keywords = {Linear partial differential equation, Asymptotics, Algorithm, Differential algebra, Formal power series, Tangent cone algorithm}, Number = {8}, Pages = {771-791}, Title = {Generalized power series solutions to linear partial differential equations}, URL = {https://www.sciencedirect.com/science/article/pii/S0747717107000442}, Volume = {42}, Year = {2007}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0747717107000442}, bdsk-url-2 = {https://doi.org/10.1016/j.jsc.2007.04.001}, date-added = {2023-02-02 19:51:14 +0100}, date-modified = {2023-02-02 19:51:14 +0100}, doi = {10.1016/j.jsc.2007.04.001} }