A Discrete Non-Classical Operational Calculus Model with the Horadam Difference

Hubert Wysocki

doi:10.5604/0860889x.1219978

References

[1] Apostol T. M., Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra, John Wiley and Sons, New York - London 1967.
Search in Google Scholar Back to article
[2] Bittner R., On certain axiomatics for the operational calculus, ‘Bull. Acad. Polon. Sci.’ Cl. III, 1959, Vol. 7, No. 1, pp. 1-9.
Search in Google Scholar Back to article
[3] Bittner R., Operational calculus in linear spaces, ‘Studia Math.’, 1961, 20, pp. 1-18.10.4064/sm-20-1-1-18
Search in Google Scholar Back to article
[4] Bittner R., Algebraic and analytic properties of solutions of abstract differential equations, ‘Rozprawy Matematyczne’ [‘Dissertationes Math.’], 41, PWN, Warszawa 1964.
Search in Google Scholar Back to article
[5] Bittner R., Rachunek operatorów w przestrzeniach liniowych, PWN, Warszawa 1974 [Operational Calculus in Linear Spaces - available in Polish].
Search in Google Scholar Back to article
[6] Bittner R., Mieloszyk E., About eigenvalues of differential equations in the operational calculus, ‘Zeszyty Naukowe Politechniki Gdańskiej’, Matematyka XI, 1978, 285, pp. 87-99.
Search in Google Scholar Back to article
[7] Čerin Z., On sums of products of Horadam numbers, ‘Kyungpook Math. J.’, 2009, 49, pp. 483-492.10.5666/KMJ.2009.49.3.483
Search in Google Scholar Back to article
[8] Horadam A. F., Generating functions for powers of a certain generalised sequence of numbers, ‘Duke Math. J.’, 1965, 32 (3), pp. 437-446.10.1215/S0012-7094-65-03244-8
Search in Google Scholar Back to article
[9] Horadam A. F., Basic properties of a certain generalized sequence of numbers, ‘Fibonacci Quart.’, 1965, 3 (3), pp. 161-176.
Search in Google Scholar Back to article
[10] Horadam A. F., Jacobsthal and Pell curves, ‘Fibonacci Quart.’, 1988, 26 (1), pp. 77-83.
Search in Google Scholar Back to article
[11] Horadam A. F., Jacobsthal representation numbers, ‘Fibonacci Quart.’, 1996, 34 (1), pp. 40-54.
Search in Google Scholar Back to article
[12] Horzum T., Kocer E. G., On some properties of Horadam polynomials, ‘Int. Math. Forum’, 2009, 4 (25), pp. 1243-1252.10.1007/s10114-009-8077-8
Search in Google Scholar Back to article
[13] Kalman D., Mena R., The Fibonacci numbers - exposed, ‘Math. Magazine’, 2003, 76 (3), pp. 167-181.10.1080/0025570X.2003.11953176
Search in Google Scholar Back to article
[14] Mansour T., A formula for the generating functions of powers of Horadam’s sequence, ‘Australas. J. Combin.’, 2004, 30, pp. 207-212.
Search in Google Scholar Back to article
[15] Mikusiński J., Operational Calculus, Pergamon Press, London 1959.
Search in Google Scholar Back to article
[16] Weisstein E. W., ‘Horadam Sequence’, From MathWorld - A Wolfram Web Resource, [online], http://mathworld.wolfram.com/HoradamSequence.html [access 12.04.2016].
Search in Google Scholar Back to article

A Discrete Non-Classical Operational Calculus Model with the Horadam Difference

References

Paradigm

My account