Special Functions
Cyclic families, sequence constructions, reciprocal structure, and exact methods.
Completion: Reading edition complete · Lean: Selected results recorded · Confidence: Recorded formal evidence
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Suggested background: Begin with the introduction and glossary. Then use the volume's own definitions to identify the background needed for its subject.
Recorded results and limits: Proofread reading volumes plus 465 named theorem declarations: 39 inherited finite-core names and 29, 21, 19, 16, 13, 19, 23, 22, 16, 34, 22, 26, 43, 27, 36, 30, 30 in Blocks01 through 17. Registered F.1-F.3, G.1, guarded G.2, named ancillary F, main H.1 and J mathematical evaluation/normalization/finite arrays are complete. J now also has an exact guarded-majorant algorithm specification with explicit resource failures and abstract validation order; successful returns certify actual bounds and endpoints. Full Python runtime/dictionary refinement remains open. Ordinary type convergence is conditional. Other J/F/H, I and A-E remain; no whole-book percentage is established.
Remaining work: Compose typed certified-evaluation metadata, tail and endpoint fields from the proved arrays and guarded majorant, then establish actual Python source/runtime/dictionary refinement with explicit assumptions; retain other J/F/H, I and A-E.
The background advice is an editorial starting point. The work itself states its prerequisites and hypotheses.
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Complete demonstration with runnable code: Komorebi sequence shapes · Stirling, Bell, and Fubini.
Explore Special Functions
Books, five families, and the coupled-function lab
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