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"rationale": "it preserves the existing rational reference selection without extending its mesh. Integer degrees belong to the Legendre recurrence and half-integer degrees to toroidal harmonics; the old independent rational arguments and third degrees are retained as bounded exploratory coverage, not special arithmetic values. Added toroidal degrees $-1/2,1/2,3/2,5/2$ use $x=\\cosh(1),\\cosh(2)$, two noncanonical low-complexity references in the separated toroidal coordinate. The value $Q_{-1/2}(3)$ is also included because its complete elliptic-integral parameter is $1/2$. The real type-3 branch for $x>1$ is used throughout",
"sources": [
"https://dlmf.nist.gov/14.3",
"https://dlmf.nist.gov/14.5",
"https://dlmf.nist.gov/14.19"
],
"retained_source_sha256": {
"generate.py": "dffa4652e00a04ef92a22edd9a06147ab36e685e11923512bdb55bf4bfcc140f"
}
}