Pith Number

pith:V7O4J5KN

pith:2017:V7O4J5KNZAYSVFJWHOGIJ5ICNT

not attested not anchored not stored refs pending

Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions

Gerg\H{o} Nemes

arxiv:1707.08175 v3 · 2017-07-22 · 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{V7O4J5KNZAYSVFJWHOGIJ5ICNT}

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	2026-05-18T00:17:27.204744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afddc4f54dc8312a95363b8c84f5026cd8730e0ebc679e7de844da06b73332fe

Aliases

arxiv: 1707.08175 · arxiv_version: 1707.08175v3 · doi: 10.48550/arxiv.1707.08175 · pith_short_12: V7O4J5KNZAYS · pith_short_16: V7O4J5KNZAYSVFJW · pith_short_8: V7O4J5KN

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/V7O4J5KNZAYSVFJWHOGIJ5ICNT \
  | 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: afddc4f54dc8312a95363b8c84f5026cd8730e0ebc679e7de844da06b73332fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "781906d1a0c0c2d6e38eb5abc74ce2b884ef287f680e9fc7f872543508ba9a6d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-07-22T09:21:50Z",
    "title_canon_sha256": "41c012562f46d91e722d34c162184b33b1b6507e04d9ceee35a29785874b176d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.08175",
    "kind": "arxiv",
    "version": 3
  }
}