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The Jinc- function: a note on the relevant generalizations and applications

Yıl 2024, , 37 - 49, 16.12.2024
https://doi.org/10.33205/cma.1507441

Öz

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.

Kaynakça

  • 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).
Yıl 2024, , 37 - 49, 16.12.2024
https://doi.org/10.33205/cma.1507441

Öz

Kaynakça

  • 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).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Yöntemler ve Özel Fonksiyonlar
Bölüm Makaleler
Yazarlar

Alessandro Curcio 0000-0002-1777-5078

G. Dattoli 0000-0003-0244-8434

Emanuele Di Palma 0000-0002-6257-622X

Erken Görünüm Tarihi 16 Aralık 2024
Yayımlanma Tarihi 16 Aralık 2024
Gönderilme Tarihi 1 Temmuz 2024
Kabul Tarihi 13 Ekim 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

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. Aralık 2024;7(Special Issue: AT&A):37-49. doi:10.33205/cma.1507441
Chicago Curcio, Alessandro, G. Dattoli, ve Emanuele Di Palma. “The Jinc- Function: A Note on the Relevant Generalizations and Applications”. Constructive Mathematical Analysis 7, sy. Special Issue: AT&A (Aralık 2024): 37-49. https://doi.org/10.33205/cma.1507441.
EndNote Curcio A, Dattoli G, Di Palma E (01 Aralık 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, ve E. Di Palma, “The Jinc- function: a note on the relevant generalizations and applications”, CMA, c. 7, sy. Special Issue: AT&A, ss. 37–49, 2024, doi: 10.33205/cma.1507441.
ISNAD Curcio, Alessandro vd. “The Jinc- Function: A Note on the Relevant Generalizations and Applications”. Constructive Mathematical Analysis 7/Special Issue: AT&A (Aralık 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 vd. “The Jinc- Function: A Note on the Relevant Generalizations and Applications”. Constructive Mathematical Analysis, c. 7, sy. Special Issue: AT&A, 2024, ss. 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.