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Discrete complementary exponential and sine integral functions

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Discrete analogues of the sine integral and complementary exponential integral functions are investigated. Hypergeometric representation, power series, and Laplace transforms are derived for each. The difficulties in extending these definitions to other common trigonometric integral functions are discussed.
Wydawca
Rocznik
Strony
art. no. 20230119
Opis fizyczny
Bibliogr. 17 poz., rys., wykr.
Twórcy
autor
  • College of Arts & Sciences, American University of Iraq-Baghdad, Sulaimani-Kirkuk Rd, Sulaymaniyah 46001, Iraq
autor
  • Department of Mathematics and Physics, Marshall University, 1 John Marshall Drive, Huntington, WV 25755 USA
Bibliografia
  • [1] J. M. Davis, I. A. Gravagne, B. J. Jackson, R. J. Marks II, and A. A. Ramos, The Laplace transform on time scales revisited, J. Math. Anal. Appl. 332 (2007), no. 2, 1291–1307.
  • [2] B. J. Jackson, A general linear systems theory on time scales: transforms, stability, and control, Baylor University, Waco, Texas, 2007.
  • [3] M. Bohner and T. Cuchta, The Bessel difference equation, Proc. Amer. Math. Soc. 145 (2017), no. 4, 1567–1580.
  • [4] A. Slavík, Discrete Bessel functions and partial difference equations, J. Difference Equ. Appl. 24 (2018), no. 3, 425–437.
  • [5] M. Bohner and T. Cuchta, The generalized hypergeometric difference equation, Demonstr. Math. 51 (2018), no. 1, 62–75.
  • [6] T. Cuchta, D. Grow, and Nick Wintz, Discrete matrix hypergeometric functions, J. Math. Anal. Appl. 518 (2023), no. 2, Paper No. 126716, 14.
  • [7] G. A. Monteiro and A. SlavÍk, Generalized elementary functions, J. Math. Anal. Appl. 411 (2014), no. 2, 838–852.
  • [8] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhäuser Boston, Inc., Boston, MA, 2001, An introduction with applications.
  • [9] M. Bohner, G. S. Guseinov, and B. Karpuz, Properties of the Laplace transform on time scales with arbitrary graininess, Integral Transforms Spec. Funct. 22 (2011), no. 11, 785–800.
  • [10] M. Bohner, G. S. Guseinov, and B. Karpuz, Further properties of the Laplace transform on time scales with arbitrary graininess, Integral Transforms Special Funct. 24 (2013), no. 4, 289–301.
  • [11] A. P. Prudnikov and O. I. Marichev, Integrals and Series: Direct Laplace Transforms, vol. 4, CRC Press, Boca Raton, Florida, USA, 1992.
  • [12] K. Oldham, J. Myland, and J. Spanier, An atlas of functions, 2nd ed., Springer, New York, 2009, With Equator, the atlas function calculator, With 1 CD-ROM (Windows).
  • [13] F. Mainardi and E. Masina, On modifications of the exponential integral with the Mittag-Leffler function, Fract. Calc. Appl. Anal. 21 (2018), no. 5, 1156–1169.
  • [14] R. J. Marks II, I. A. Gravagne, J. M. Davis, and J. J. DaCunha, Nonregressivity in switched linear circuits and mechanical systems, Math. Comput. Modell. 43 (2006), no. 11–12, 1383–1392.
  • [15] M. Bohner and G. S. Guseinov, An introduction to complex functions on products of two time scales, J. Difference Equations Appl. 12 (2006), no. 3–4, 369–384.
  • [16] S. Smirnov, Discrete complex analysis and probability, Proceedings of the International Congress of Mathematicians, Vol. I, Hindustan Book Agency, New Delhi, 2010, pp. 595–621.
  • [17] L. Lovász, Discrete analytic functions: an exposition, Surveys in Differential Geometry, vol. 9, Int. Press, Somerville, MA, 2004, pp. 241–273.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0f194a58-ec1f-4607-9c28-0595a32f9e0f
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