Pith Number

pith:OJHAB2WB

pith:2026:OJHAB2WBXXVFKOTTRUXKTTGHV6

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Analytic summation of series involving higher-order derivatives of Chebyshev polynomials of the second kind and their applications to convolved linear recurrent sequences

Alexander Stokolos, Daniel Gray, Dmitriy Dmitrishin, Vitaly Khamitov

Series of higher-order derivatives of Chebyshev polynomials of the second kind sum analytically to rational functions expressed in the polynomials.

arxiv:2605.03200 v3 · 2026-05-04 · math.CV · math.CO · math.NT

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\usepackage{pith}
\pithnumber{OJHAB2WBXXVFKOTTRUXKTTGHV6}

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Record completeness

1 Bitcoin timestamp

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

Analytic summation determines the rational functions to which these series converge; these functions are expressed in terms of Chebyshev polynomials evaluated at a specific argument, yielding new closed-form formulas for sums at various values and combinatorial identities for Fibonacci, Lucas, and Pell numbers and their convolutions.

C2weakest assumption

That the relation between polynomial degree and derivative order, together with the analytic properties of Chebyshev polynomials of the second kind, permits term-by-term differentiation and summation inside the disk of convergence without additional justification for the specific series considered.

C3one line summary

Analytic summation yields closed forms for series of higher derivatives of Chebyshev polynomials of the second kind, giving identities for convolved linear recurrent sequences including Fibonacci numbers.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:09:58.868529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

724e00eac1bdea553a738d2ea9ccc7af89055cc26c19f8c0d14ea9bafcbbbd41

Aliases

arxiv: 2605.03200 · arxiv_version: 2605.03200v3 · doi: 10.48550/arxiv.2605.03200 · pith_short_12: OJHAB2WBXXVF · pith_short_16: OJHAB2WBXXVFKOTT · pith_short_8: OJHAB2WB

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/OJHAB2WBXXVFKOTTRUXKTTGHV6 \
  | 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: 724e00eac1bdea553a738d2ea9ccc7af89055cc26c19f8c0d14ea9bafcbbbd41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf97c16b509b8ddc9c45186e21113fd3ed62208f7356c31ca2bc0641938ab57d",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-04T22:36:00Z",
    "title_canon_sha256": "6b33fabf84711eca23078519518a69436b4eec38e53a66746fe6fe648155d8fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03200",
    "kind": "arxiv",
    "version": 3
  }
}