$d$-Orthogonality of $q$-Sheffer Polynomials

Serhan Varma; Eylül Emine Göçmez

doi:10.31801/cfsuasmas.1648887

$d$-Orthogonality of $q$-Sheffer Polynomials

Abstract

In this paper, we find necessary and sufficient conditions for $q$-Sheffer polynomials to be $d$-orthogonal. Moreover, an example is presented and with the help of this example, we rediscover some known $d$-orthogonal polynomial sets.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Serhan Varma ^*
0000-0003-0346-5738
Türkiye

Eylül Emine Göçmez This is me
0009-0008-0781-4759
Türkiye

Early Pub Date

February 2, 2026

Publication Date

February 2, 2026

Submission Date

February 28, 2025

Acceptance Date

December 24, 2025

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.31801/cfsuasmas.1648887

IZ

https://izlik.org/JA36MX68FL

Cite

RIS / Bibtex

APA

Varma, S., & Göçmez, E. E. (2026). $d$-Orthogonality of $q$-Sheffer Polynomials. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Advanced Online Publication, 1-8. https://doi.org/10.31801/cfsuasmas.1648887

AMA

1.Varma S, Göçmez EE. $d$-Orthogonality of $q$-Sheffer Polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;(Advanced Online Publication):1-8. doi:10.31801/cfsuasmas.1648887

Chicago

Varma, Serhan, and Eylül Emine Göçmez. 2026. “$d$-Orthogonality of $q$-Sheffer Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, no. Advanced Online Publication: 1-8. https://doi.org/10.31801/cfsuasmas.1648887.

EndNote

Varma S, Göçmez EE (February 1, 2026) $d$-Orthogonality of $q$-Sheffer Polynomials. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Advanced Online Publication 1–8.

IEEE

[1]S. Varma and E. E. Göçmez, “$d$-Orthogonality of $q$-Sheffer Polynomials”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., no. Advanced Online Publication, pp. 1–8, Feb. 2026, doi: 10.31801/cfsuasmas.1648887.

ISNAD

Varma, Serhan - Göçmez, Eylül Emine. “$d$-Orthogonality of $q$-Sheffer Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. Advanced Online Publication (February 1, 2026): 1-8. https://doi.org/10.31801/cfsuasmas.1648887.

JAMA

1.Varma S, Göçmez EE. $d$-Orthogonality of $q$-Sheffer Polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;:1–8.

MLA

Varma, Serhan, and Eylül Emine Göçmez. “$d$-Orthogonality of $q$-Sheffer Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, no. Advanced Online Publication, Feb. 2026, pp. 1-8, doi:10.31801/cfsuasmas.1648887.

Vancouver

1.Serhan Varma, Eylül Emine Göçmez. $d$-Orthogonality of $q$-Sheffer Polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026 Feb. 1;(Advanced Online Publication):1-8. doi:10.31801/cfsuasmas.1648887