The Jinc- function: a note on the relevant generalizations and applications
Year 2024,
Volume: 7 Issue: Special Issue: AT&A, 37 - 49, 16.12.2024
Alessandro Curcio
,
G. Dattoli
,
Emanuele Di Palma
Abstract
Jinc and sinc-functions are well known special functions with important applications in Spectral theory, Fourier Optics and diffraction problems from circular apertures. The first are less widespread known than the latter and should be more properly framed within the context of special functions. In this article we present a unified point of view to the relevant generalizations, propose generalized forms and touch on application perspectives.
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Year 2024,
Volume: 7 Issue: Special Issue: AT&A, 37 - 49, 16.12.2024
Alessandro Curcio
,
G. Dattoli
,
Emanuele Di Palma
References
- E. W. Weisstein: Jinc Function,From MathWorld–A Wolfram Web Resource, https://mathworld.wolfram.com/
JincFunction.html
- R. Bracewell, P. B. Kahn: The Fourier transform and its applications American Journal of Physics, 34 (8) (1966), 712.
- Y. Li, E.Wolf: Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers, J. Opt. Soc. Am. A, 1 (8) (1984), 801-–808.
- L. C. Andrews: Special functions for engineers and applied mathematicians, Macmillan, USA (1985).
- A. E. Siegman: Lasers, University Science Books, USA (1986).
- W. i. R. Hendee, P. N. T. Wells: The Perception of Visual Information, Springer, New York (1997).
- G. E. Andrews, R. Askey and R. Roy: Special Functions, Cambridge University Press, Cambridge (1999).
- M. Born, E. Wolf: Principles of Optics, Cambridge University Press, Cambridge (1999).
- Q. Cao: Generalized Jinc functions and their application to focusing and diffraction of circular apertures, J. Opt. Soc. Am. A, 20 (4) (2003), 661–667.
- R. E. Blahut: Theory of remote image formation, Cambridge University Press, Cambridge (2004).
- K. B. Oldham, J. Myland and J. Spanier: An Atlas of Functions: with Equator, the Atlas Function Calculator, Springer New York (2010).
- D. Babusci, G. Dattoli, K. Górska and K. A. Penson: The spherical Bessel and Struve functions and operational methods, Appl. Math. Comput., 238 (2014), 1–6.
- G. Dattoli, E. Di Palma, S. Licciardi and E. Sabia: From Circular to Bessel Functions: A Transition through the Umbral Method, Fractal and Fractional, 1 (1) (2017), Article ID: 9.
- D. Babusci, G. Dattoli, S. Licciardi and E. Sabia: Mathematical Metods for Physicists, World Scientific, Singapur
(2019).
- S. Licciardi, G. Dattoli: Guide to the Umbral Calculus. World Scientific, Singapur (2022).