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Such a generalization takes the form \\[\n  \\left({}^{\\rho}\\mathcal{I}^{\\alpha, \\beta}_{a+;\\eta, \\kappa}f\\right)(x)=\\frac{\\rho^{1-\\beta}x^{\\kappa}}{\\Gamma(\\alpha)}\\int_a^x \\frac{\\tau^{\\rho \\eta +\\rho-1}}{(x^\\rho-\\tau^\\rho)^{1-\\alpha}}f(\\tau)\\text{d}\\tau, \\quad 0\\leq a < x < b \\leq \\infty. \\] A similar generalization is not possible with the Erd\\'elyi-Kober operator though"},"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":"1612.08596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-22T16:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"6f77036b571c1e075273b367f7b095272d16a39410d9e6604d0ac9f61e2c9a4a","abstract_canon_sha256":"c887bc543f602d8e0d6c2e826ce06e382e3342f2f3dbbfa55c271f8cab4781ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:52.579254Z","signature_b64":"7CHkjfjNI0NpWmALu8G3sMqdpK3/sOuo3GI0hVTFwY6IcjhoBIiCQcB/eP4DadEAp83pKkhhpqumdgnhCZbKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47f80e8a01b31bb64dbe307455e9483923e7d1c09bcc95c755415a1157849e2b","last_reissued_at":"2026-05-18T00:53:52.578650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:52.578650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New fractional integral unifying six existing fractional integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Udita N. 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