Theory and application of the generalized difference operator of the n-th kind (part I)

• Autorzy: Susai Manuel M. M. , Xavier G. B. A. , Chandrasekar V. , Pugalarasu R.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the authors extend the theory of the generalized difference operator (…) .to the generalized difference operator of the n-th kind denoted by (…), where L =(…)of positive reals (…) and obtain some intresting results on the relation between the generalized polynomial factorial of the first kind, n-th kind and algebraic polynomials. Also formulae for the sum of general partial sums of products of several powers of consecutive terms of an arithmetic progression in number theory are derived.

Słowa kluczowe

EN

generalized difference operator; generalized factorial; partial sums

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 1
• Strony: 94--106
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Susai Manuel M. M.

autor

Xavier G. B. A.

autor

Chandrasekar V.

autor

Pugalarasu R.

• Department Of Science And Humanities R.M.D. Engineering College Kavaraipettai - 601 206, Tamil Nadu, S. India,

Bibliografia

• [1] R. P Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 2000.
• [2] M. Maria Susai Manuel, G. Britto Antony Xavier, E. Thandapani, Theory of generalized difference operator and its applications, Far East J. Math. Sci. 20(2) (2006), 163–171.
• [3] M. Maria Susai Manuel, G. Britto Antony Xavier, E. Thandapani, Qualitative properties of solutions of certain class of difference equations , Far East J. Math. Sci. 23 (3) (2006), 295–304.
• [4] M. Maria Susai Manuel, G. Britto Antony Xavier, E. Thandapani, Generalized Bernoulli polynomials through weighted pochhammer symbols, Far East J. Appl. Math. 26 (3) (2007), 321–333.
• [5] M. Maria Susai Manuel, A. George Maria Selvam, G. Britto Antony Xavier, Rotatory and boundedness of solutions of certain class of difference equations, Int. J. Pure Appl. Math. 33(3) (2006), 333–343.
• [6] M. Maria Susai Manuel, G. Britto Antony Xavier, Recessive, dominant and spiral behaviours of solutions of certain class of generalized difference equations, Int. J. Differ. Equ. Appl. 10(4) (2007), 423–433.
• [7] M. Maria Susai Manuel, G. Britto Antony Xavier, V. Chandrasekar, Generalized difference operator of the second kind and its application to number theory, Int. J. Pure Appl. Math. 47(1) (2008), 127–140.
• [8] M. Maria Susai Manuel, G. Britto Antony Xavier, V. Chandrasekar, R. Pugalarasu, S. Elizabeth, On generalized difference operator of third kind and its applications in number theory, Int. J. Pure Appl. Math. 53(1), (2009), 69–81.
• [9] R. E. Mickens, Difference Equations, Van Nostrand Reinhold Company, New York, 1990.
• [10] S. N. Elaydi, An Introduction to Difference Equations, 2nd ed., Springer, 1999.
• [11] W. G. Kelley, A. C. Peterson, Difference Equations. An Introduction with Applica-tions, Academic Press, inc 1991.