back to table · edit · history · where entries came from · files · download
13053 bytes, as of the version from 2026-10-27 01:07 (current). Recorded here, not run.
{
"table": "T207",
"entries": 38,
"controls": [
"integral(t^2,0,3)=9",
"integral(exp(-t),0,1)=1-exp(-1)",
"Ai(0) gamma identity",
"exact erf/erfc/Fresnel origins",
"independent mpmath polynomial quadrature"
],
"records": [
{
"argument": "0",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": null,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(2)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1103,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "2",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1104,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(6)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(8)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(10)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(12)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(14)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "4",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1104,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(18)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(20)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1100,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(22)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(24)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1100,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(26)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(28)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1100,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(30)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(32)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1100,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(34)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "6",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1104,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(38)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(40)",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1100,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "1",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1104,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(3)",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1103,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(5)",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(7)",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "3",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1104,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(11)",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(13)",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(15)",
"family": "paired-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "sqrt(1/2)",
"family": "diagonal-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "1*sqrt(2/pi)",
"family": "unit-quadratic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": "independent finite-interval mpmath quadrature at 170 dps"
},
{
"argument": "sqrt(3/2)",
"family": "diagonal-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1103,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "2*sqrt(2/pi)",
"family": "unit-quadratic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": "independent finite-interval mpmath quadrature at 170 dps"
},
{
"argument": "sqrt(5/2)",
"family": "diagonal-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1103,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "3*sqrt(2/pi)",
"family": "unit-quadratic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": "independent finite-interval mpmath quadrature at 170 dps"
},
{
"argument": "sqrt(7/2)",
"family": "diagonal-cornu",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1102,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "4*sqrt(2/pi)",
"family": "unit-quadratic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": "independent finite-interval mpmath quadrature at 170 dps"
},
{
"argument": "1/2",
"family": "simple-fresnel",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1104,
"root_bracket_checked": false,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
}
],
"versions": {
"numberdb": "0.1.10",
"python-flint": "0.6.0",
"mpmath": "1.3.0"
},
"source_sha256": {
"balanced_values.py": "1333dc603c1a65159dbffe7c263998a058f74537e1d8e961468339b0291e2d1a",
"balanced_checks.py": "875e34e73c5c5937623ab19f780d00c47330ac87242729f279b0e7fc7f0a44d3"
},
"structure": {
"all_original_entries_identical": true,
"all_original_comments_identical": true,
"parameter_order_preserved": true,
"complete_generator_enumeration": true,
"new_arguments_exactly_deduplicated": true,
"new_unresolved_citations": [],
"entries_block_bytes": 8795,
"retained_count": 21,
"added_count": 17
}
}