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Here we show that both the integrals are very special cases of the family of (real) functions $$ I(\\lambda,\\mu,\\nu; z) :=\\int_0^zx^{\\lambda}\\,\\Enu(x^{\\mu})\\,dx= {\\gamma\\left({1+\\lambda\\over\\mu},z^{\\mu}\\right) + z^{1+\\lambda}\\Enu(z^{\\mu})\\over 1+\\lam"},"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":"2009.06452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-14T14:08:22Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"4367274f2191b707ee07fd7fffde8c788487413ea72be2bce2f0b17774a54154","abstract_canon_sha256":"6300a4ff483f41a5f2248b565dcf22b204cf9956f41115afca628cc5d761a316"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:35:08.795177Z","signature_b64":"sHqHr3c54krlHOozdeDJ8+rLXWq6dBNa1m/QsphPDmthYKtcB5JgOCakGkd0S2yvvnlil8LbnL3oCrW0Y7MlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e1169d26a1b799c0d493d8a1a0d6f841a225e0e41f043ad49a59b6594a38c1d","last_reissued_at":"2026-07-05T01:35:08.794832Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:35:08.794832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A family of Exponential Integrals suggested by Stellar Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Astronomy, Italy), Luca Ciotti (Dept. of Physics, University of Bologna","submitted_at":"2020-09-14T14:08:22Z","abstract_excerpt":"While investigating the generalization of the Chandrasekhar (1943) dynamical friction to the case of field stars with a power-law mass spectrum and equipartition Maxwell-Boltzmann velocity distribution, a pair of 2-dimensional integrals involving the Error function occurred, with closed form solution in terms of Exponential Integrals (Ciotti 2010). 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