Finite bivariate biorthogonal I - Konhauser polynomials

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Güldoğan Lekesi̇z E., ÇEKİM B., Özarslan M. A.

Journal of Computational and Applied Mathematics, cilt.476, 2026 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 476
• Basım Tarihi: 2026
• Doi Numarası: 10.1016/j.cam.2025.117106
• Dergi Adı: Journal of Computational and Applied Mathematics
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
• Anahtar Kelimeler: Finite biorthogonal polynomial, Fourier transform, Fractional operator, Konhauser polynomial, Laplace transform, Mittag-Leffler function
• Gazi Üniversitesi Adresli: Evet

Özet

In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval's identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.