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An operational calculus model for the central difference and exponential-trigonometric and hyperbolic fibonacci sequences


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[1] Apostol T. M., Calculus, Vol. 1, One-Variable Calculus, with an Introduction to Linear Algebra, John Wiley & Sons, New York — London 1967.Search in Google Scholar

[2] Bittner R., On certain axiomatics for the operational calculus, ‘Bull. Acad. Polon. Sci.’, Cl. III, 1959, 7(1), pp. 1–9.Search in Google Scholar

[3] Bittner R., Operational calculus in linear spaces, ‘Studia Math.’, 1961, 20, pp. 1–18.10.4064/sm-20-1-1-18Search in Google Scholar

[4] Bittner R., Algebraic and analytic properties of solutions of abstract differential equations, ‘Rozprawy Matematyczne’ [‘Dissertationes Math.’], 42, PWN, Warszawa 1964.Search in Google Scholar

[5] Bittner R., Rachunek operatorów w przestrzeniach liniowych, PWN, Warszawa 1974 [Operational Calculus in Linear Spaces — available in Polish].Search in Google Scholar

[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

[7] Elaydi S., An Introduction to Difference Equations, Springer Sci. & Business Media, New York 2005.Search in Google Scholar

[8] Falcón S., Plaza A., On the Fibonacci k-numbers, ‘Chaos, Solitons and Fractals’, 2007, 32(5), pp. 1615–1624.10.1016/j.chaos.2006.09.022Search in Google Scholar

[9] Gazalé M. J., Gnomon: From Pharaohs to Fractals, Princeton Univ. Press, New Jersey 1999.Search in Google Scholar

[10] Jordan Ch., Calculus of Finite Differences, Chelsea Publ. Comp., New York 1950.Search in Google Scholar

[11] Kalman D., Mena R., The Fibonacci numbers — exposed, ‘Math. Magazine’, 2003, 76(3), pp. 167–181.10.1080/0025570X.2003.11953176Search in Google Scholar

[12] Levy H., Lessman F., Finite Difference Equations, Pitman & Sons, London 1959.Search in Google Scholar

[13] Mathews J. H., Fink K. D., Numerical Methods Using MATLAB, Prentice Hall, New Jersey 1999.Search in Google Scholar

[14] Mercer P. R., More Calculus for a Single Variable, Springer Sci. & Business Media, New York 2014.10.1007/978-1-4939-1926-0Search in Google Scholar

[15] Mikusiński J., Operational Calculus, Pergamon Press, London 1959.Search in Google Scholar

[16] Spinadel V. W., The Family of Metallic Means, ‘VisMath — Visual Mathematics’, Electronic Journal, 1999, Vol. 1(3) [online], http://www.mi.sanu.ac.rs/vismath/spinadel/index.html [access 14.06.2018].Search in Google Scholar

[17] Spinadel V. W., New Smarandache Sequences: The Family of Metallic Means [online], http://vixra.org/abs/1403.0507 [access 14.06.2018].Search in Google Scholar

[18] Stakhov A., The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science, Series of Knots and Everything: Vol. 22, World Scientific, Singapore 2009.10.1142/6635Search in Google Scholar

[19] Stakhov A., Rozin B., On a new class of hyperbolic functions, ‘Chaos, Solitons and Fractals’, 2005, 23(2), pp. 379–389.10.1016/j.chaos.2004.04.022Open DOISearch in Google Scholar

[20] Washburn L., The Lanczos derivative, Senior Project Archive 2006, Dept. of Maths., Whitman College, USA, [online], https://www.whitman.edu/Documents/Academics/Mathematics/washbuea.pdf [access 14.06.2018].Search in Google Scholar

[21] Wysocki H., Spira Mirabilis in the selected models of the Bittner operational calculus, ‘Zeszyty Naukowe Akademii Marynarki Wojennej’ [‘Scientific Journal of PNA’], 2015, 4(203), pp. 65–96.10.5604/0860889X.1187627Search in Google Scholar

[22] Wysocki H., An operational calculus model for the nth-order forward difference, ‘Zeszyty Naukowe Akademii Marynarki Wojennej’ [‘Scientific Journal of PNA’], 2017, 3(210), pp. 107–117.10.5604/01.3001.0010.6593Search in Google Scholar