{"paper":{"title":"Analytical transit light curves for arbitrary power-law limb darkening: a unified framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","astro-ph.SR"],"primary_cat":"astro-ph.EP","authors_text":"Farrukh A. Chishtie, Mohammad I. Saeed, Shaukat N. Goderya","submitted_at":"2025-06-23T17:22:11Z","abstract_excerpt":"We present a unified analytical framework for computing exoplanet transit light curves under arbitrary real power-law limb darkening $I(\\mu)=I_0\\mu^\\alpha$, $\\alpha>-2$, eliminating the two-decade restriction to integer-polynomial forms. Our central result is an exact closed-form expression for the normalised stellar flux in terms of Appell's bivariate hypergeometric function $F_1$, valid for all real $\\alpha$ and all geometric transit configurations. Three mutually equivalent formulations -- a geometric kernel representation, a Riemann-Liouville fractional-calculus framework, and a hypergeome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18860","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.18860/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}