balanced-selection.json

back to table · edit · history · where entries came from · files · download

11106 bytes, as of the version from 2026-10-27 01:11 (current). Recorded here, not run.

{
  "tid": "T494",
  "kind": "struvel",
  "parameters": [
    "nu",
    "x"
  ],
  "rows": [
    {
      "params": {
        "nu": "0",
        "x": "0"
      },
      "argument": {
        "type": "rational",
        "value": "0"
      },
      "entry": "0",
      "origin": "retained website entry",
      "digits": 100
    },
    {
      "params": {
        "nu": "0",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "entry": "0.7102431859378908887385266778116507449444099583297031981230151655739691156882381809773540391579117258",
      "origin": "retained website entry",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "0"
      },
      "argument": {
        "type": "rational",
        "value": "0"
      },
      "entry": "0",
      "origin": "retained website entry",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "entry": "0.2267643810558086368261753538677918847361832955676687095737719815374595587599634353384819291648013737",
      "origin": "retained website entry",
      "digits": 100
    },
    {
      "params": {
        "nu": "0",
        "x": "1/2"
      },
      "argument": {
        "type": "rational",
        "value": "1/2"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "0.3272406993941807802475218143697526013249599983276467039800203277942434941612902357400114406001067032",
      "digits": 100
    },
    {
      "params": {
        "nu": "0",
        "x": "2"
      },
      "argument": {
        "type": "rational",
        "value": "2"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "1.937433757991445661161521326319693095686482529772495335358244701075522654352853696364746933831895688",
      "digits": 100
    },
    {
      "params": {
        "nu": "0",
        "x": "3"
      },
      "argument": {
        "type": "rational",
        "value": "3"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "4.648685731753710282598935769061639910923351238852300918232542604589111528137790184294552446159375729",
      "digits": 100
    },
    {
      "params": {
        "nu": "0",
        "x": "5"
      },
      "argument": {
        "type": "rational",
        "value": "5"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "27.10591712655814655322253488178511411832852843862841621443402639646847522074929510289108766028968053",
      "digits": 100
    },
    {
      "params": {
        "nu": "0",
        "x": "8"
      },
      "argument": {
        "type": "rational",
        "value": "8"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "427.4830347130955659684785419034990276600709411724531929317205241146519112272799317812809950566015203",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "1/2"
      },
      "argument": {
        "type": "rational",
        "value": "1/2"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "0.05394218262352266329233324711166140172769854724645848875528433177768845699476837411978483823558464379",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "2"
      },
      "argument": {
        "type": "rational",
        "value": "2"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "1.102759787367715817589721650181908914811889696943731540829103646297867070648572235328031286632879281",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "3"
      },
      "argument": {
        "type": "rational",
        "value": "3"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "3.396612947474775997751454161593429909992653904405835989738612020939423300702031647964535431124464143",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "5"
      },
      "argument": {
        "type": "rational",
        "value": "5"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "23.72821578040828244582709544174408094553749528639606432144708483918569428100611959050728406077193052",
      "digits": 100
    },
    {
      "params": {
        "nu": "1",
        "x": "8"
      },
      "argument": {
        "type": "rational",
        "value": "8"
      },
      "role": "low-order sine or hyperbolic-sine integral reference",
      "origin": "balanced expansion",
      "entry": "399.2470913872569767243187488725777172921478814420467418663025269390845424503485882574378444355723965",
      "digits": 100
    },
    {
      "params": {
        "nu": "2",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "role": "unit argument along integer and half-integer order recurrences",
      "origin": "balanced expansion",
      "entry": "0.04450783303707983406099761891271449275943050620709051397858141042052093465600926351357177713997153058",
      "digits": 100
    },
    {
      "params": {
        "nu": "3",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "role": "unit argument along integer and half-integer order recurrences",
      "origin": "balanced expansion",
      "entry": "0.006291730749650544377149207984263417155938698541851600660068381439670007433465971926831139867247761756",
      "digits": 100
    },
    {
      "params": {
        "nu": "4",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "role": "unit argument along integer and half-integer order recurrences",
      "origin": "balanced expansion",
      "entry": "0.0006944030880567454830972752596096331748665189277730453039742705802572025262905163301044121168181758143",
      "digits": 100
    },
    {
      "params": {
        "nu": "1/2",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "role": "unit argument along integer and half-integer order recurrences",
      "origin": "balanced expansion",
      "entry": "0.4333156537901020906259996225857388668956874487678961059711137653576900787515395272455748988118907898",
      "digits": 100
    },
    {
      "params": {
        "nu": "3/2",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "role": "unit argument along integer and half-integer order recurrences",
      "origin": "balanced expansion",
      "entry": "0.1054169540539528781513172018712726324602430728988563515102636745183963607243954799857875372312671174",
      "digits": 100
    },
    {
      "params": {
        "nu": "5/2",
        "x": "1"
      },
      "argument": {
        "type": "rational",
        "value": "1"
      },
      "role": "unit argument along integer and half-integer order recurrences",
      "origin": "balanced expansion",
      "entry": "0.01732922152788528668706150198832550239599357228009338702384128438483651510352762766289920364126270352",
      "digits": 100
    },
    {
      "params": {
        "nu": "1/2",
        "x": "2"
      },
      "argument": {
        "type": "rational",
        "value": "2"
      },
      "role": "elementary half-order reference",
      "origin": "balanced expansion",
      "entry": "1.558402036629880906868040844170805355275075030324819532014648653133900936400331887783237575453884640",
      "digits": 100
    },
    {
      "params": {
        "nu": "1/2",
        "x": "3"
      },
      "argument": {
        "type": "rational",
        "value": "3"
      },
      "role": "elementary half-order reference",
      "origin": "balanced expansion",
      "entry": "4.177098891899722153709735552969182767831135537748051558296065688484478298806581825694150578488146055",
      "digits": 100
    },
    {
      "params": {
        "nu": "1/2",
        "x": "5"
      },
      "argument": {
        "type": "rational",
        "value": "5"
      },
      "role": "elementary half-order reference",
      "origin": "balanced expansion",
      "entry": "26.12312694107539649757170348530765125212182101705424329562852806331331278691578930115127063832361290",
      "digits": 100
    }
  ],
  "baseline_revision": "91e6dcc5fa99ee8371a3090dbf556fa3e6dec2975dd9d3f648f31cfcce14ec65",
  "baseline_captured_utc": "2026-10-27T00:49:02.630916+00:00",
  "rationale": "it preserves all existing values and uses the integral-representation pair of orders $0,1$ at $x=0,1/2,1,2,3,5,8$, with orders $2,3,4,1/2,3/2,5/2$ at $x=1$ and order $1/2$ also at $x=2,3,5$. The integer-order recurrences and elementary half-order formulas give structural breadth. The positive radii are sparse, bounded exploratory references for the sine or hyperbolic-sine integrals, not a mesh or documented demand for every argument. Exact origin values remain exact",
  "sources": [
    "https://dlmf.nist.gov/11.2",
    "https://dlmf.nist.gov/11.4",
    "https://dlmf.nist.gov/11.5"
  ],
  "retained_source_sha256": {
    "T494-repair-checks.json": "ea7a66e785cf427d6a6e7a0d4540b260475622b10c91d0ef4f508e092517503e",
    "audit.json": "cfd42dff735add81476ec75e40df543c15e49b515a04844b4a768759c961fe88",
    "check.py": "1b69965212b74b8e9fa1d38b507f5629f9f4319707aefcf0bcb0dc94a6fb611b",
    "check_t494_repair.py": "58c2ef4aa0d2cd6cfe6c9b8baf28ef7667fda343b5f378a643f63e3257dd094a",
    "checks-evidence.json": "10c8ddf7bef5cd8f1099c4e2ddfbdfc62727f452110307a63a9dcabceb3e802f",
    "checks-offline-summary.json": "6e532b3743d16e1f3d971e29322033c628f2f563809a51e1b940ed37069c8250",
    "checks-stored-summary.json": "6515544cf918f397adfcf897b863e6b76d50e2f5a4098bd90be2b7525b871ca4",
    "checks.py": "d493ae7f6d9548dfdafc50940c3bc2a14062f66ed0b6511f86a3bc0d4e281785",
    "generate.py": "76f51b0f5d09b648ad6b7ffd8e137255ded39350099fd297e32947d21ca5ad4a",
    "intrinsic_values.py": "9abda9287522297eea7668269d83aca3dc63e4c6385120fd663ff40d2310e184",
    "numerical-evidence.json": "e89ca2fa4ed1c20e66b6f28f123a0e9c8a0a912225c5c1297df1a9ed3ec647a4",
    "program-checks.log": "a8f8628ff5309ff2dcfe1337f9f45562e578e2bd9a0af7b0724310e81d5cbd0c",
    "selection.json": "4105b5b1f0d7d0eeaf737e5447c544e1bde91633e63f287ba871c61739d3bd67",
    "selection.md": "64b1655bcfb8b148b214cf34688161b09793002a7650583c96b0b0f1340467fd",
    "versions.json": "486a8aa2ef9f5cd7c49eda9b2fe5d7e938a05e7c29184d146b3c1b1ff504bc79"
  }
}