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1638 bytes, as of the version from 2026-10-27 01:13 (current). Recorded here, not run.
# Primary sources for T490
Read through the web tool on 2026-10-25:
* https://dlmf.nist.gov/10.61, equation 10.61.1: ber + i bei equals J at x exp(3 pi i/4), and also exp(nu pi i/2) times I at x exp(pi i/4). Equations 10.61.5 and 10.61.6 give argument and order reflection. The integer-order case has no branch point at zero.
* https://dlmf.nist.gov/10.63, equation 10.63.2: f_(nu-1)+f_(nu+1) = -nu sqrt(2)(f_nu-g_nu)/x, with the ordered pair (ber,bei).
* https://dlmf.nist.gov/10.65, equation 10.65.1: the cosine-weighted power series used by checks.py, with Gamma(n+k+1) replaced by (n+k)! for the stored integer orders.
* https://dlmf.nist.gov/10.64, equation 10.64.1: the Schlaefli integral used by checks.py. Replacing the source's argument x sqrt(2) with the stored argument requires dividing its internal x by sqrt(2).
The web responses identify DLMF version 1.2.8 (2026-09-15). Raw HTML downloads from the build machine returned HTTP 403, but the web tool retrieved and exposed the equations successfully. No inaccessible numerical dataset was used.
The family conventions were read from numberdb-data issue 205 and preserved in family-205.md. The local and live skills were compared; their differences concern argument selection and statistical tables, not the Kelvin definition. The argument selection retains the family's small-denominator rational rectangle, rather than replacing it with a decimal grid. The upper range and the absence of zero follow the family. The family's sentence saying ker is finite at zero was not adopted: ker_0 is logarithmically singular, as the next clause in that same sentence acknowledges.