selection.json

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2934 bytes, as of the version from 2026-10-27 01:14 (current). Recorded here, not run.

{
  "tid": "T491",
  "kind": "bei",
  "rationale": "These are intrinsic extremal heights, with the finite origin limit where it exists. The exact argument is the unique zero of the derivative in the explicitly listed rational interval. The intervals identify roots; their endpoints are not evaluation arguments. Six isolated critical arguments are retained per selected order. Numbering orders this finite selection, without claiming a global count of all preceding zeros. The order-zero Kelvin functions are the standard ber, bei, ker, kei functions. ",
  "unresolved": "No external application is asserted for these individual extremal heights; their relevance is intrinsic.",
  "sources": [
    "https://dlmf.nist.gov/10.61",
    "https://dlmf.nist.gov/10.63"
  ],
  "rows": [
    {
      "params": {
        "nu": "0",
        "x": "0"
      },
      "argument": "0",
      "reason": "Continuous initial value, not a sampling argument."
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-1"
      },
      "argument": "critical",
      "bracket": [
        "3863/1024",
        "483/128"
      ],
      "label": "$c_{1}$",
      "reason": "Intrinsic extremal height; the index labels the specified isolating interval, not a global zero count."
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-2"
      },
      "argument": "critical",
      "bracket": [
        "8479/1024",
        "265/32"
      ],
      "label": "$c_{2}$",
      "reason": "Intrinsic extremal height; the index labels the specified isolating interval, not a global zero count."
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-3"
      },
      "argument": "critical",
      "bracket": [
        "13047/1024",
        "1631/128"
      ],
      "label": "$c_{3}$",
      "reason": "Intrinsic extremal height; the index labels the specified isolating interval, not a global zero count."
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-4"
      },
      "argument": "critical",
      "bracket": [
        "8803/512",
        "17607/1024"
      ],
      "label": "$c_{4}$",
      "reason": "Intrinsic extremal height; the index labels the specified isolating interval, not a global zero count."
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-5"
      },
      "argument": "critical",
      "bracket": [
        "1385/64",
        "22161/1024"
      ],
      "label": "$c_{5}$",
      "reason": "Intrinsic extremal height; the index labels the specified isolating interval, not a global zero count."
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-6"
      },
      "argument": "critical",
      "bracket": [
        "26713/1024",
        "13357/512"
      ],
      "label": "$c_{6}$",
      "reason": "Intrinsic extremal height; the index labels the specified isolating interval, not a global zero count."
    }
  ]
}