Generalized sequences with applications to the discrete calculus
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- Math. Comp. 19 (1965), 177-200 Request permission
References
- E. T. Bell, Euler algebra, Trans. Amer. Math. Soc. 25 (1923), no. 1, 135–154. MR 1501234, DOI 10.1090/S0002-9947-1923-1501234-1
- Lothar Berg, Einführung in die Operatorenrechnung, Mathematik für Naturwissenschaft und Technik, Band 6, VEB Deutscher Verlag der Wissenschaften, Berlin, 1962 (German). MR 0141952
- George Boole, Calculus of finite differences, Chelsea Publishing Co., New York, 1957. Edited by J. F. Moulton 4th ed. MR 0115025 W. S. Brown, J. P. Hyde, & B. A. Tague, "The ALPAK system for nonnumerical algebra on a digital computer. II. Rational functions on several variables," Bell System Tech. J., v. 43, 1964, pp. 785–804.
- Ruel V. Churchill, Operational mathematics, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. 2nd ed. MR 0108696
- J. L. B. Cooper, Heaviside and the operational calculus, Math. Gaz. 36 (1952), 5–19. MR 45641, DOI 10.2307/3610762 H. T. Davis, The Theory of Linear Operators, Principia Press, Bloomington, Indiana, 1936. J. Eliáš, "On an operator method for difference equations" (Czech), Mat.-Fys.Časopis. Sloven. Akad. Vied., v. 8, 1958, pp. 203–227. MR 21#4312.
- Arthur Erdélyi, Operational calculus and generalized functions, Holt, Rinehart and Winston, New York, 1962. MR 0142990
- L. Feldmann, On linear difference equations with constant coefficients, Period. Polytech. Elec. Engrg. 3 (1959), 247–257. MR 110901
- Tomlinson Fort, Linear difference equations and the Dirichlet series transform, Amer. Math. Monthly 62 (1955), 641–645. MR 76181, DOI 10.2307/2307288
- E. T. Frankel, A calculus of figurate numbers and finite differences, Amer. Math. Monthly 57 (1950), 14–25. MR 33265, DOI 10.2307/2305169 C. Jordan, Calculus of Finite Differences, Chelsea, New York, 1950.
- Wilfred Kaplan, Operational methods for linear systems, Addison-Wesley Series in Mathematics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1962. MR 0139903
- Kaiser S. Kunz, Numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1957. MR 0088045
- D. F. Lawden, On the solution of linear difference equations, Math. Gaz. 36 (1952), 193–196. MR 50151, DOI 10.2307/3608257
- Jan Mikusiński, Operational calculus, International Series of Monographs on Pure and Applied Mathematics, Vol. 8, Pergamon Press, New York-London-Paris-Los Angeles; Państwowe Wydawnictwo Naukowe, Warsaw, 1959. MR 0105594
- L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan & Co., Ltd., London, 1951. MR 0043339
- D. H. Moore, Convolution products and quotients and algebraic derivatives of sequences, Amer. Math. Monthly 69 (1962), 132–138. MR 136942, DOI 10.2307/2312544
- John Riordan, An introduction to combinatorial analysis, Wiley Publications in Mathematical Statistics, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096594
- Selmo Tauber and Donald Dean, On difference equations containing step and delta functions, J. Soc. Indust. Appl. Math. 8 (1960), 174–180. MR 115028 J. S. Zypkin, Differenzenrechnungen der Impulse und Regeltechnik (Translated from Russian), Verlag Technik, Berlin, 1956.
Additional Information
- © Copyright 1965 American Mathematical Society
- Journal: Math. Comp. 19 (1965), 177-200
- MSC: Primary 39.10
- DOI: https://doi.org/10.1090/S0025-5718-1965-0179489-9
- MathSciNet review: 0179489