back to table · edit · history · where entries came from · files · download
10848 bytes, as of the version from 2026-10-27 01:14 (current). Recorded here, not run.
{
"tid": "T493",
"kind": "ker",
"parameters": [
"nu",
"x"
],
"rows": [
{
"params": {
"nu": "0",
"x": "critical-1"
},
"argument": {
"type": "critical",
"bracket": [
"2729/1024",
"1365/512"
]
},
"entry": {
"number": "-0.07102369095680270647635516160943273306644359264953390224653038475549433817676674892330197815157953917",
"param-latex": "$c_{1}$"
},
"origin": "retained website entry",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "critical-2"
},
"argument": {
"type": "critical",
"bracket": [
"459/64",
"7345/1024"
]
},
"entry": {
"number": "0.001956680996778300827967657275632605256495707844071242680703457303514297085779293986130477409219808882",
"param-latex": "$c_{2}$"
},
"origin": "retained website entry",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "critical-3"
},
"argument": {
"type": "critical",
"bracket": [
"11911/1024",
"1489/128"
]
},
"entry": {
"number": "-0.00006705968998387590537846511459767901894891739463036061278751943649105400268000561805054315741116817836",
"param-latex": "$c_{3}$"
},
"origin": "retained website entry",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "critical-4"
},
"argument": {
"type": "critical",
"bracket": [
"16469/1024",
"8235/512"
]
},
"entry": {
"number": "0.000002475318422703877880871956555313340357202960739158092840055782554878267551495965643822253424186024740",
"param-latex": "$c_{4}$"
},
"origin": "retained website entry",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "critical-5"
},
"argument": {
"type": "critical",
"bracket": [
"21023/1024",
"657/32"
]
},
"entry": {
"number": "-9.490862856667466088940117769028334473518237475398557805267463193248935009018897734105282925138196439e-8",
"param-latex": "$c_{5}$"
},
"origin": "retained website entry",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "critical-6"
},
"argument": {
"type": "critical",
"bracket": [
"3197/128",
"25577/1024"
]
},
"entry": {
"number": "3.724326080038865710796054190985712103394332030127294207527392537186324988675506166396482870689818507e-9",
"param-latex": "$c_{6}$"
},
"origin": "retained website entry",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "1/2"
},
"argument": {
"type": "rational",
"value": "1/2"
},
"role": "order-zero sparse reference radii, not a mesh",
"origin": "balanced expansion",
"entry": "0.8559058721186342136915945279433104322245850538580413530645346713052975415097998566728847334855656116",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "1"
},
"argument": {
"type": "rational",
"value": "1"
},
"role": "order-zero sparse reference radii, not a mesh",
"origin": "balanced expansion",
"entry": "0.2867062087283160459541973148723017754490240033608223594900948463792722614169513200022850758591711337",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "2"
},
"argument": {
"type": "rational",
"value": "2"
},
"role": "order-zero sparse reference radii, not a mesh",
"origin": "balanced expansion",
"entry": "-0.04166451399150953225868222391388440386260607077490109870726262695644441770741760499024945635786291633",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "3"
},
"argument": {
"type": "rational",
"value": "3"
},
"role": "order-zero sparse reference radii, not a mesh",
"origin": "balanced expansion",
"entry": "-0.06702923330379869775199782194748322134382113006988930954248646894121370966598911962993220960911582965",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "5"
},
"argument": {
"type": "rational",
"value": "5"
},
"role": "order-zero sparse reference radii, not a mesh",
"origin": "balanced expansion",
"entry": "-0.01151172719949066247036165702465553933688891845717020987695907173212846116417775830292940567693315048",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "8"
},
"argument": {
"type": "rational",
"value": "8"
},
"role": "order-zero sparse reference radii, not a mesh",
"origin": "balanced expansion",
"entry": "0.001485834068518962537290258298041040714610243708591313869072803265554151749033800252119514166413375079",
"digits": 100
},
{
"params": {
"nu": "0",
"x": "sqrt(2)"
},
"argument": {
"type": "scaled_sqrt",
"factor": "1",
"radicand": "2"
},
"role": "equal real/imaginary rotated Bessel arguments at integer scale",
"origin": "balanced expansion",
"label": "$\\sqrt{2}$",
"entry": {
"number": "0.08019772694651781872696873656427916683407726210094976913653468259584576126030427112728932350137784080",
"param-latex": "$\\sqrt{2}$"
},
"digits": 100
},
{
"params": {
"nu": "0",
"x": "2*sqrt(2)"
},
"argument": {
"type": "scaled_sqrt",
"factor": "2",
"radicand": "2"
},
"role": "equal real/imaginary rotated Bessel arguments at integer scale",
"origin": "balanced expansion",
"label": "$2\\sqrt{2}$",
"entry": {
"number": "-0.06997380475897996320301621182079731956769266180063395639172346941622576476315508719693786776430922195",
"param-latex": "$2\\sqrt{2}$"
},
"digits": 100
},
{
"params": {
"nu": "0",
"x": "4*sqrt(2)"
},
"argument": {
"type": "scaled_sqrt",
"factor": "4",
"radicand": "2"
},
"role": "equal real/imaginary rotated Bessel arguments at integer scale",
"origin": "balanced expansion",
"label": "$4\\sqrt{2}$",
"entry": {
"number": "-0.003111921278091821848645337123704753019740170741657930190055001825348199832727845594324728640443890513",
"param-latex": "$4\\sqrt{2}$"
},
"digits": 100
},
{
"params": {
"nu": "1",
"x": "1"
},
"argument": {
"type": "rational",
"value": "1"
},
"role": "unit argument for adjacent integer orders and elementary half order",
"origin": "balanced expansion",
"entry": "-0.7403222768419827101138729208464400876081945355986875182364200545555667776979531665124743162644226609",
"digits": 100
},
{
"params": {
"nu": "2",
"x": "1"
},
"argument": {
"type": "rational",
"value": "1"
},
"role": "unit argument for adjacent integer orders and elementary half order",
"origin": "balanced expansion",
"entry": "0.4180336179440250228240823346537054356322252536790457263424099082740615442676999194594330649624840419",
"digits": 100
},
{
"params": {
"nu": "3",
"x": "1"
},
"argument": {
"type": "rational",
"value": "1"
},
"role": "unit argument for adjacent integer orders and elementary half order",
"origin": "balanced expansion",
"entry": "4.887273882413628733035327535946384371261651349624461349582064859673351287220986814094998834218600963",
"digits": 100
},
{
"params": {
"nu": "1/2",
"x": "1"
},
"argument": {
"type": "rational",
"value": "1"
},
"role": "unit argument for adjacent integer orders and elementary half order",
"origin": "balanced expansion",
"entry": "-0.1911092250400757080075088839756047214022363532646147829110591281305315807579739382224484236907197255",
"digits": 100
},
{
"params": {
"nu": "1",
"x": "2"
},
"argument": {
"type": "rational",
"value": "2"
},
"role": "order-one companion for radial derivative relations",
"origin": "balanced expansion",
"entry": "-0.2308059295181229630209686472211253422891005958599114548363780469203562879219468897135833112267940182",
"digits": 100
}
],
"baseline_revision": "7963478640818cbfff238191ccd62cb3673aa5a2b42c0323c5fda861a345070e",
"baseline_captured_utc": "2026-10-27T00:49:01.865282+00:00",
"rationale": "it preserves the existing order-zero extremal heights and finite initial value where present. Order zero gains the sparse references $x=1/2,1,2,3,5,8$ and $x=\\sqrt2,2\\sqrt2,4\\sqrt2$. The latter give equal integer-sized real and imaginary components in the rotated Bessel argument; this is a normalization-based reference, not a universal physical scale. Orders $1,2,3,1/2$ are sampled only at $x=1$, with order $1$ also at $x=2$, to cover adjacent integer-order relations and the elementary half-order reduction. These finite exploratory slices avoid a Cartesian grid and make no demand claim for each radius",
"sources": [
"https://dlmf.nist.gov/10.61",
"https://dlmf.nist.gov/10.63",
"https://dlmf.nist.gov/10.73"
],
"retained_source_sha256": {
"check.py": "1b69965212b74b8e9fa1d38b507f5629f9f4319707aefcf0bcb0dc94a6fb611b",
"checks-evidence.json": "3bc9884605e9867088e0cfa937d6e100d09774f6f5c80550d2e6e30df895f3c9",
"checks.py": "d493ae7f6d9548dfdafc50940c3bc2a14062f66ed0b6511f86a3bc0d4e281785",
"generate.py": "27df605ad637cba0cc500a9390fa8b1b7dad8471caedfef2d71d5ea6f8bd73a3",
"intrinsic_values.py": "9abda9287522297eea7668269d83aca3dc63e4c6385120fd663ff40d2310e184",
"repair-evidence.json": "c71c29f545444fb4fd1ee95458060d58590641cdad7c6fed0bd5520411695d33",
"repair_checks.py": "0e8eb26e1382c47b1725a5df401a234480068409e2b76b352b779b0d7bc5d8a3",
"selection.json": "b9e768d346014102f563783c31d5ff375360394b44e4973548a3a36fc753ba00",
"selection.md": "985dae48dac5cc864b92ff025f102ededd14d3a9233513e4d72f91ed403f3e27"
},
"critical_source_sha256": "9abda9287522297eea7668269d83aca3dc63e4c6385120fd663ff40d2310e184"
}