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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
https://doi.org/10.33205/cma.1507441

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.

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).
Year 2024, Volume: 7 Issue: Special Issue: AT&A, 37 - 49, 16.12.2024
https://doi.org/10.33205/cma.1507441

Abstract

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).
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Methods and Special Functions
Journal Section Articles
Authors

Alessandro Curcio 0000-0002-1777-5078

G. Dattoli 0000-0003-0244-8434

Emanuele Di Palma 0000-0002-6257-622X

Early Pub Date December 16, 2024
Publication Date December 16, 2024
Submission Date July 1, 2024
Acceptance Date October 13, 2024
Published in Issue Year 2024 Volume: 7 Issue: Special Issue: AT&A

Cite

APA Curcio, A., Dattoli, G., & Di Palma, E. (2024). The Jinc- function: a note on the relevant generalizations and applications. Constructive Mathematical Analysis, 7(Special Issue: AT&A), 37-49. https://doi.org/10.33205/cma.1507441
AMA Curcio A, Dattoli G, Di Palma E. The Jinc- function: a note on the relevant generalizations and applications. CMA. December 2024;7(Special Issue: AT&A):37-49. doi:10.33205/cma.1507441
Chicago Curcio, Alessandro, G. Dattoli, and Emanuele Di Palma. “The Jinc- Function: A Note on the Relevant Generalizations and Applications”. Constructive Mathematical Analysis 7, no. Special Issue: AT&A (December 2024): 37-49. https://doi.org/10.33205/cma.1507441.
EndNote Curcio A, Dattoli G, Di Palma E (December 1, 2024) The Jinc- function: a note on the relevant generalizations and applications. Constructive Mathematical Analysis 7 Special Issue: AT&A 37–49.
IEEE A. Curcio, G. Dattoli, and E. Di Palma, “The Jinc- function: a note on the relevant generalizations and applications”, CMA, vol. 7, no. Special Issue: AT&A, pp. 37–49, 2024, doi: 10.33205/cma.1507441.
ISNAD Curcio, Alessandro et al. “The Jinc- Function: A Note on the Relevant Generalizations and Applications”. Constructive Mathematical Analysis 7/Special Issue: AT&A (December 2024), 37-49. https://doi.org/10.33205/cma.1507441.
JAMA Curcio A, Dattoli G, Di Palma E. The Jinc- function: a note on the relevant generalizations and applications. CMA. 2024;7:37–49.
MLA Curcio, Alessandro et al. “The Jinc- Function: A Note on the Relevant Generalizations and Applications”. Constructive Mathematical Analysis, vol. 7, no. Special Issue: AT&A, 2024, pp. 37-49, doi:10.33205/cma.1507441.
Vancouver Curcio A, Dattoli G, Di Palma E. The Jinc- function: a note on the relevant generalizations and applications. CMA. 2024;7(Special Issue: AT&A):37-49.