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Demonstratio Mathematica

Tytuł artykułu

The nabla difference model of the operational calculus

Autorzy Wysocki, H. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
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
PL symbol nabla   rachunek operatorowy   rachunek operatorówy Bittnera   pochodna   wzór Taylora  
EN nabla symbol   operational calculus   Bittner operational calculus   derivative   Taylor's formula  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 2
Strony 315--326
Opis fizyczny Bibliogr. 12 poz.
autor Wysocki, H.
[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,
[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.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-6708c7dc-9023-4ec5-89db-c2f7f578d2a0