Pith Number

pith:UGLXOS24

pith:2016:UGLXOS24TEDNHVDT6PNSAIF6GS

not attested not anchored not stored refs pending

Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions

Gerg\H{o} Nemes

arxiv:1606.07961 v2 · 2016-06-25 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UGLXOS24TEDNHVDT6PNSAIF6GS}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:40:51.685329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a197774b5c9906d3d473f3db2020be34ba9e3aaeb786b5c4619c908fcef0ebf5

Aliases

arxiv: 1606.07961 · arxiv_version: 1606.07961v2 · doi: 10.48550/arxiv.1606.07961 · pith_short_12: UGLXOS24TEDN · pith_short_16: UGLXOS24TEDNHVDT · pith_short_8: UGLXOS24

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UGLXOS24TEDNHVDT6PNSAIF6GS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a197774b5c9906d3d473f3db2020be34ba9e3aaeb786b5c4619c908fcef0ebf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7546dd608b9c14dae29b2ec895324a315169e190edc3dc4daaf9959ff8b837db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-06-25T20:22:06Z",
    "title_canon_sha256": "22375f92a3240c739a8e4e491a005ed49dcd3bb24d124c78ab425d12dd5ce4f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07961",
    "kind": "arxiv",
    "version": 2
  }
}