{"paper":{"title":"Computer aided solution of the invariance equation for two-variable Stolarsky means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Szabolcs Baj\\'ak, Zsolt P\\'ales","submitted_at":"2012-11-24T22:37:06Z","abstract_excerpt":"We solve the so-called invariance equation in the class of two-variable Stolarsky means ${S_{p,q}:p,q\\in\\R}$, i.e., we find necessary and sufficient conditions on the 6 parameters $a,b,c,d,p,q$ such that the identity [S_{p,q}\\big(S_{a,b}(x,y),S_{c,d}(x,y)\\big)=S_{p,q}(x,y) \\qquad (x,y \\in \\R_+)] be valid. We recall that, for $pq(p-q)\\neq 0$ and $x\\neq y$, the Stolarsky mean $S_{p,q}$ is defined by [S_{p,q}(x,y):=(\\dfrac{q(x^p-y^p)}{p(x^q-y^q)})^{\\frac1{p-q}}.] In the proof first we approximate the Stolarsky mean and we use the computer algebra system Maple V Release 9 to compute the Taylor exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6100","kind":"arxiv","version":2},"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"}