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pith:PDOKDBOK

pith:2026:PDOKDBOK5E3TXD227TJB7BIPD4

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Fourier representations of fractional B Splines via generalized Stirling type polynomials

Damla Gun, Peter Massopust, Yilmaz Simsek

Fractional B-splines admit a Fourier expansion in generalized Stirling-type numbers that represents them as infinite sums of Dirac delta derivatives in the distributional sense.

arxiv:2605.15244 v1 · 2026-05-14 · math.GM

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Claims

C1strongest claim

Our main contribution is the derivation of a Fourier-type expansion of fractional B splines in terms of generalized Stirling-type numbers. This representation allows us to express fractional B splines as infinite linear combinations of derivatives of the Dirac delta in the distributional sense.

C2weakest assumption

The generating function approach inspired by recent results of Simsek [24] extends directly to fractional B-splines to produce the claimed Fourier expansion and distributional representation (abstract, main contribution paragraph).

C3one line summary

Derives Fourier representations of fractional B-splines via generalized Stirling-type polynomials, yielding distributional expressions with Dirac deltas and new fractional spline polynomials generated by the Mittag-Leffler function.

References

28 extracted · 28 resolved · 0 Pith anchors

[1] T. Agoh, K. Dilcher, Shortened recurrence relations for Bernoulli numbers, Discrete Math. 309 (2009) 887–898 2009

[2] Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht, 1974 (translated from French by J 1974

[3] Akhiezer, ¨Uber die beste Ann¨ aherung einer Klasse stetiger periodischer Funktionen, Dokl 1937

[4] T. Blu, M. Unser, Approximation error for quasi-interpolators and (multi-)wavelet expansions, Appl. Comput. Harmon. Anal. 6 (2000) 219–251 2000

[5] Dana-Picard, Integral presentations of Catalan numbers and Wallis formula, Int 2011

Formal links

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Receipt and verification

First computed	2026-05-20T00:00:48.142312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78dca185cae9373b8f5afcd21f850f1f00a50b2b8da81b421315d024764fa643

Aliases

arxiv: 2605.15244 · arxiv_version: 2605.15244v1 · doi: 10.48550/arxiv.2605.15244 · pith_short_12: PDOKDBOK5E3T · pith_short_16: PDOKDBOK5E3TXD22 · pith_short_8: PDOKDBOK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PDOKDBOK5E3TXD227TJB7BIPD4 \
  | 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: 78dca185cae9373b8f5afcd21f850f1f00a50b2b8da81b421315d024764fa643

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03bd9afddc5c17efa0a30e45b69159a768ee7cac4fd9267e9bec799a680f5006",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-05-14T07:43:08Z",
    "title_canon_sha256": "8fcf74e046b68fbe691191d13ed2d5a991e179677757d08494817bbba63fd451"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15244",
    "kind": "arxiv",
    "version": 1
  }
}