{"paper":{"title":"Using sums of squares to prove that certain entire functions have only real zeros","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"George Gasper Jr","submitted_at":"1993-07-09T00:00:00Z","abstract_excerpt":"It is shown how sums of squares of real valued functions can be used to give new proofs of the reality of the zeros of the Bessel functions $J_\\alpha (z)$ when $\\alpha \\ge -1,$ confluent hypergeometric functions ${}_0F_1(c\\/; z)$ when $c>0$ or $0>c>-1$, Laguerre polynomials $L_n^\\alpha(z)$ when $\\alpha \\ge -2,$ and Jacobi polynomials $P_n^{(\\alpha,\\beta)}(z)$ when $\\alpha \\ge -1$ and $ \\beta \\ge -1.$ Besides yielding new inequalities for $|F(z)|^2,$ where $F(z)$ is one of these functions, the derived identities lead to inequalities for $\\partial |F(z)|^2/\\partial y$ and $\\partial ^2 |F(z)|^2/\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9307210","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"}