{"paper":{"title":"Spectral parameter power series for arbitrary order linear differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CA","authors_text":"R. Michael Porter, Sergii M. Torba, Vladislav V. Kravchenko","submitted_at":"2017-12-18T23:19:51Z","abstract_excerpt":"Let $L$ be the $n$-th order linear differential operator $Ly = \\phi_0y^{(n)} + \\phi_1y^{(n-1)} + \\cdots + \\phi_ny$ with variable coefficients. A representation is given for $n$ linearly independent solutions of $Ly=\\lambda r y$ as power series in $\\lambda$, generalizing the SPPS (spectral parameter power series) solution which has been previously developed for $n=2$. The coefficient functions in these series are obtained by recursively iterating a simple integration process, begining with a solution system for $\\lambda=0$. It is shown how to obtain such an initializing system working upwards f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06717","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}