Pith Number

pith:RMHMCR5E

pith:2026:RMHMCR5E7LITE6I5T56LQIP6UF

not attested not anchored not stored refs pending

On a $_2F_1\big(\frac{1}{4}\big)$-identity due to Gosper

Cetin Hakimoglu-Brown

Integration on a Gosper 2F1 identity produces a gamma closed form for a hypergeometric series at a large rational argument.

arxiv:2604.04799 v2 · 2026-04-06 · math.CA

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\pithnumber{RMHMCR5E7LITE6I5T56LQIP6UF}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We present a new and integration-based approach toward the construction of special values for 2F1-series of the desired form. We apply this approach using a 2F1(1/4)-identity originally due to Gosper ... to evaluate a 2F1-series of convergence rate (172872/185039)^2.

C2weakest assumption

That the proposed integration-based construction actually produces a valid closed-form evaluation in terms of gamma values for the specific series considered, without hidden assumptions about convergence or analytic continuation.

C3one line summary

A new integration approach is used to evaluate a 2F1 series at argument (172872/185039)^2, extending a Gosper identity and claiming the largest numerator/denominator among known strange evaluations.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-08T01:04:03.875399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b0ec147a4fad132791d9f7cb821fea16cb4b52a2e155fd264fcc5f89cd45f63

Aliases

arxiv: 2604.04799 · arxiv_version: 2604.04799v2 · doi: 10.48550/arxiv.2604.04799 · pith_short_12: RMHMCR5E7LIT · pith_short_16: RMHMCR5E7LITE6I5 · pith_short_8: RMHMCR5E

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/RMHMCR5E7LITE6I5T56LQIP6UF \
  | 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: 8b0ec147a4fad132791d9f7cb821fea16cb4b52a2e155fd264fcc5f89cd45f63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f9ac0edd38198d14ecf1c9afad1628fb90fd0218faabc61264ecdb6debe4540",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-04-06T16:05:46Z",
    "title_canon_sha256": "f4e899a79c4010245c87f7ac1fac8e57201919758f00f1be3906f106e0d29eb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.04799",
    "kind": "arxiv",
    "version": 2
  }
}