The nabla difference model of the operational calculus

• Autorzy: Wysocki H.
• Języki publikacji: EN

Abstrakty

EN

In the paper, there has been constructed the (...)-model of the Bittner operational calculus for the backward difference (…) in the space of two-sided sequences. A form of the Taylor’s formula has been derived. Applying the operation (...), the (...)-model has been generalized.

Słowa kluczowe

EN

nabla symbol; operational calculus; Bittner operational calculus; derivative; Taylor's formula

PL

symbol nabla; rachunek operatorowy; rachunek operatorówy Bittnera; pochodna; wzór Taylora

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 2
• Strony: 315--326
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Wysocki H.

• Chair of Mathematics and Physics, Polish Naval Academy, Śmidowicza St 69, 81-103 Gdynia, Poland

Bibliografia

• [1] R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Marcel Dekker, New York, 2000.
• [2] D. R. Anderson, Taylor polynomials for nabla dynamic equations on time scales, Pan Amer. Math. J. 12(4) (2002), 17–27.
• [3] R. Bittner, On certain axiomatics for the operational calculus, Bull. Acad. Polon. Sci. III 7(1) (1959), 1–9.
• [4] R. Bittner, Algebraic and Analytic Properties of Solutions of Abstract Differential Equations, Dissertationes Math. 41, PWN – Polish Scientific Publishers, Warszawa, 1964.
• [5] R. Bittner, Operational Calculus in Linear Spaces (in polish), PWN – Polish Scientific Publishers, Warszawa, 1974.
• [6] I. H. Dimovski, V. S. Kiryakova, Discrete operational calculi for two-sided sequences, The Fibonacci Quarterly (Proc. 5th Internat. Conf. on Fibonacci Numbers and Their Applications), 5 (1993), 159–168.
• [7] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, New York, 1988.
• [8] D. E. Knuth, Negafibonacci numbers and the hyperbolic plane, Pi Mu Epsilon J. Sutherland Frame Lecture at „MathFest 2007”, San José, CA, 2007-08-04, http://www.pme-math.org/conferences/national/2007/2007.html.
• [9] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Inc., New York, 2001.
• [10] H. Levy, F. Lessman, Finite Difference Equations, Pitman and Sons, London, 1959.
• [11] S. Roman, The Umbral Calculus, Academic Press, Orlando, FL, 1984.
• [12] H. Wysocki, Taylor’s formula for the forward difference via operational calculus, Studia Sci. Math. Hungar. 47(1) (2010), 46–53.