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Since one-sided L\\'evy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions $\\rho_\\alpha(x)$ of the latter. We show, however, that the formula is computationally inviable for fractions with large denominators, being unpractical even for some modest values of $l$ and $k$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1106.0531","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-06-02T23:15:37Z","cross_cats_sorted":[],"title_canon_sha256":"f5a06e7e59f8cb4aeb794e4fece80d02f32a25bad7be89a4c730f4c0c5c49056","abstract_canon_sha256":"a56243709619f48694c9bb11a9ae76e6c8b748695c75ce56875b2824d6cb06a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:11.583695Z","signature_b64":"Bo5JEsiEEALenO/8Tmt6vg2RiIbb8aFOiIsxGDIcyKQaNYYGhZk1jN1unY/Be8bi387Yc7l4EBJvchoj/81iDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05796fbe40aa3539d74db6cd74fdaaff54c9012983f6639127a776af8acfac63","last_reissued_at":"2026-05-18T04:16:11.583203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:11.583203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alberto Saa, Roberto Venegeroles","submitted_at":"2011-06-02T23:15:37Z","abstract_excerpt":"We consider here the recently proposed closed form formula in terms of the Meijer G-functions for the probability density functions $g_\\alpha(x)$ of one-sided L\\'evy stable distributions with rational index $\\alpha=l/k$, with $0<\\alpha<1$. Since one-sided L\\'evy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions $\\rho_\\alpha(x)$ of the latter. 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