Integral representations of Apostol-type splines: approach to generating function method of special polynomials

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GÜN D.

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, cilt.120, sa.3, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 120 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s13398-026-01855-z
  • Dergi Adı: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Apostol-type polynomials, B-spline moments, Beta and gamma functions, Catalan numbers, Generating functions, Integral representations, Special functions, Spline, Stirling numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The purpose of this paper is to give moment formulas with the aid of Milovanović [16]. Other aims are to establish new integral formulas in order to define new Apostol-type splines in terms of the Apostol-type polynomials. By the aid of these integral formulas, we derive a novel class of moment-type expressions arising from integrals of these polynomials. By applying generating function techniques and moment computations, we derive explicit representations and approximation formulas for Apostol- Bernoulli, Euler, and Frobenius spline polynomials. Closed-form expansions are established using Goldman’s formula and symbolic moment identities. The connection between cardinal B-splines ϕn(x) and uniform B-splines N0,n-1(x) is given. We compute integrals using beta-type representations and provide recurrence relations for numerical implementation. Furthermore, we develop a comparative numerical table that confirms the validity of the approximation.