Binomial Transform Technique For Solving Linear Difference Equations
DOI:
https://doi.org/10.29304/jqcm.2021.13.2.815Keywords:
difference equations, linear difference equations, Binomial transformAbstract
Our goal in this paper is to find a new transformation technique for solving linear difference equations, as in the case of Z-transformation. And we were able to find the binomial transform, and this transform is one of the most common transformations. The linear difference equations can be solved by the binomial transformation.
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References
H. . Poincaré, Sur les equations linéaires aux différentielles ordinaires et aux differences finies, Amer. J. Math. 7 (1885), 203-258.
Jerri, Abdul J.," Linear Difference Equations With Discrete Transform Methods", Kluwer Academic Publishers, 1996.
Miclcnes,R.E."Difference Equations. Theory Applications and advanced Topics", 3^ed ed. Champam & Hall , 2015.
Elaydi, S.N. "An introduction to difference equations" , Springer, 2^ed ed . 1999.
Kelley W.G,& Pcterson A.C." Difference Equations. An Introduction with Applications", 2^ed ed .Academic Press , 2001.
Ladas, G., Open problems and conjecture. Journal of Difference Equations and Applications, 5, 317–321, 1995.
S. Goldberg, Introduction to Difference Equations: With Illustrative Examples from Economics, Psychology and Sociology, New York: Dover Publications, Inc., 2010.
S. Weinzierl, Expansions around half-integer values, binomial sums and inverse binomial sums, J. Math. Phys. 45 (2004), 2656–2673.
Derrick Henry Lehmer, Interesting series involving the central binomial coefficient, Amer. Math. Monthly 92 (1985), 449–457.
Khristo N. Boyadzhiev, Binomial transform and the backward difference. Adv. Appl. Discrete Math., 13(1)(2014),43-63.
Khristo N. Boyadzhiev, Binomial transform of products,
Ars Comb., 126 (2016), 415 434.
K. W. Chen, Identities from the binomial transform, J. Number Theory 124(2007), 142-150.
Yan-Ping Mu, Symmetric recurrence relations and binomial transforms, J. Number Theory, 133 (2013) 3127-3137.
Mogens E. Larsen and Peter J. Larcombe, Some binomial coefficient identities of specific and general type, Util. Math., 74 (2007), 33-53.
N. YÄ´slmaz, N. Taskara, Binomial transforms of the Padovan and Perrinnumbers, Journal of Abstract and Applied Mathematics, (2013) ArticleID941673.
H. Prodinger, Some information about the binomial transform, The Fibonacci Quarterly, 32(5), 1994, 412-415.
Boyadzhiev, K. (2018). Notes on the Binomial Transform: Theory and Table with Appendix on Stirling Transform, World Scientific, Singapore.
A. Taha, B., & J. Kadhim, A. (2018). Non-polynomial spline finite difference method for solving second order boundary value problem. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), Math Page 92 - 101. https://doi.org/10.29304/jqcm.2018.10.2.384
AbdulAmeer AbdulJabbar, I., & Ali Yakoob, Z. (2018). Hybrid techniques to improve face recognition based on features extraction methods and Haar discrete wavelet transformation. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), Comp Page 36 - 46. https://doi.org/10.29304/jqcm.2018.10.2.372
Ali Mohamad, H., & Falih Jaddoa, A. (2019). Property of oscillation of first order impulsive neutral differential equations with positive and negative coefficients. Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(1), Math Page 45 - 51. https://doi.org/10.29304/jqcm.2019.11.1.457
S. Rahma, A. M., & Ayad Jabbar, D. (2019). Development cryptography protocol based on Magic Square and Linear Algebra System. Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(1), Comp Page 72 - 75. https://doi.org/10.29304/jqcm.2019.11.1.470
Hadi, A. M., & Abdulrahman, A. A. (2020). Multi Discrete Laguerre Wavelets Transforms with The Mathematical aspects. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Comp Page 26-37. https://doi.org/10.29304/jqcm.2020.12.1.672.
Jerri, Abdul J.," Linear Difference Equations With Discrete Transform Methods", Kluwer Academic Publishers, 1996.
Miclcnes,R.E."Difference Equations. Theory Applications and advanced Topics", 3^ed ed. Champam & Hall , 2015.
Elaydi, S.N. "An introduction to difference equations" , Springer, 2^ed ed . 1999.
Kelley W.G,& Pcterson A.C." Difference Equations. An Introduction with Applications", 2^ed ed .Academic Press , 2001.
Ladas, G., Open problems and conjecture. Journal of Difference Equations and Applications, 5, 317–321, 1995.
S. Goldberg, Introduction to Difference Equations: With Illustrative Examples from Economics, Psychology and Sociology, New York: Dover Publications, Inc., 2010.
S. Weinzierl, Expansions around half-integer values, binomial sums and inverse binomial sums, J. Math. Phys. 45 (2004), 2656–2673.
Derrick Henry Lehmer, Interesting series involving the central binomial coefficient, Amer. Math. Monthly 92 (1985), 449–457.
Khristo N. Boyadzhiev, Binomial transform and the backward difference. Adv. Appl. Discrete Math., 13(1)(2014),43-63.
Khristo N. Boyadzhiev, Binomial transform of products,
Ars Comb., 126 (2016), 415 434.
K. W. Chen, Identities from the binomial transform, J. Number Theory 124(2007), 142-150.
Yan-Ping Mu, Symmetric recurrence relations and binomial transforms, J. Number Theory, 133 (2013) 3127-3137.
Mogens E. Larsen and Peter J. Larcombe, Some binomial coefficient identities of specific and general type, Util. Math., 74 (2007), 33-53.
N. YÄ´slmaz, N. Taskara, Binomial transforms of the Padovan and Perrinnumbers, Journal of Abstract and Applied Mathematics, (2013) ArticleID941673.
H. Prodinger, Some information about the binomial transform, The Fibonacci Quarterly, 32(5), 1994, 412-415.
Boyadzhiev, K. (2018). Notes on the Binomial Transform: Theory and Table with Appendix on Stirling Transform, World Scientific, Singapore.
A. Taha, B., & J. Kadhim, A. (2018). Non-polynomial spline finite difference method for solving second order boundary value problem. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), Math Page 92 - 101. https://doi.org/10.29304/jqcm.2018.10.2.384
AbdulAmeer AbdulJabbar, I., & Ali Yakoob, Z. (2018). Hybrid techniques to improve face recognition based on features extraction methods and Haar discrete wavelet transformation. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), Comp Page 36 - 46. https://doi.org/10.29304/jqcm.2018.10.2.372
Ali Mohamad, H., & Falih Jaddoa, A. (2019). Property of oscillation of first order impulsive neutral differential equations with positive and negative coefficients. Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(1), Math Page 45 - 51. https://doi.org/10.29304/jqcm.2019.11.1.457
S. Rahma, A. M., & Ayad Jabbar, D. (2019). Development cryptography protocol based on Magic Square and Linear Algebra System. Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(1), Comp Page 72 - 75. https://doi.org/10.29304/jqcm.2019.11.1.470
Hadi, A. M., & Abdulrahman, A. A. (2020). Multi Discrete Laguerre Wavelets Transforms with The Mathematical aspects. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Comp Page 26-37. https://doi.org/10.29304/jqcm.2020.12.1.672.
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Published
2021-06-30
How to Cite
Hussain, D. E. A., & Jasim, A. S. (2021). Binomial Transform Technique For Solving Linear Difference Equations. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(2), Math Page 193– 202. https://doi.org/10.29304/jqcm.2021.13.2.815
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Math Articles
