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Some Properties of the Fractional Circle Zernike Polynomials

In: Integral Methods in Science and Engineering, Volume 1

Author

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  • M. M. Rodrigues

    (University of Aveiro, CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics)

  • N. Vieira

    (University of Aveiro, CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics)

Abstract

In this paper, we present a fractional extension of the classical circle Zernike polynomials defined via g-Jacobi functions. Some properties of this new class of functions are studied, such as recurrence relations for consecutive and distant neighborhoods, and differential relations. A graphic representation for the proposed fractional circle Zernike polynomials will be presented in the final section of the paper.

Suggested Citation

  • M. M. Rodrigues & N. Vieira, 2017. "Some Properties of the Fractional Circle Zernike Polynomials," Springer Books, in: Christian Constanda & Matteo Dalla Riva & Pier Domenico Lamberti & Paolo Musolino (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 0, pages 265-276, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-59384-5_24
    DOI: 10.1007/978-3-319-59384-5_24
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