On the limits of quotients of polynomials in two variables

• Autorzy: Wituła R. , Hetmaniok E. , Wróbel A. , Matlak J.

Identyfikatory

DOI

10.17512/jamcm.2015.1.12

• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to discuss different types of decompositions and factorizations concerning a few families of symmetric polynomials in two variables including Ma polynomials, classic Cauchy polynomials, Ferrers-Jackson polynomials and some elementary polynomials as well. Application of the discussed decompositions and factorizations for determining the limits of quotients of the respective polynomials in two variables is presented here and some general theorems on these limits are also proven in this elaboration.

Słowa kluczowe

EN

Cauchy polynomials; Ma polynomials; Ferrers-Jackson polynomials; limits of quotients of multivariable polynomials

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 1
• Strony: 121--132
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Wituła R.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Hetmaniok E.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Wróbel A.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

autor

Matlak J.

• Institute of Mathematics, Silesian University of Technology Gliwice, Poland

Bibliografia

• [1] Ma X., A generalization of the Kummer identity and its application to Fibonacci-Lucas sequences, The Fibonacci Quarterly 1998, 36, 339-347.
• [2] Wituła R., Hetmaniok E., Słota D., Problem 1876, Math. Magazine October 2011 issue.
• [3] Wituła R., Słota D., Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences, Central Eur. J. Math. 2006, 4, 531- 546.
• [4] Ribenboim P., Fermat's Last Theorem for Amateurs, Springer-Verlag, New York Inc., 1999.
• [5] Liu Y., Wang Y., A class of multivariable limits, College Math. Journal 2010, 41, 2, 194-196.
• [6] Choi J., Rathie A.K, New results for the series 2F1(x) with an application, Commun. Korean Math. Soc., 2014, 29, 65-74.
• [7] Wituła R., On some applications of formulae for the sum of unimodular complex numbers, Pracownia Komputerowa Jacka Skalmierskiego, Gliwice 2011.
• [8] Vajda S., Fibonacci and Lucas Numbers, and the Golden Section, Theory and Application, Dover Publications, Inc., 2008.
• [9] Hayashi N., Matusi Y., Decomposition formulae for generalized hypergeometric functions with the Gauss - Kummer identity, Commun. Korean Math. Soc., 2014, 29, 97-108.
• [10] Prudnikov A.P., Brychkov Y.A., Marichev O.I, Integrals and series. 1. Elementary functions, translated from the Russian and with a preface by N.M. Queen, Gordon & Breach Science Publishers, New York 1986.
• [11] Wituła R., Hetmaniok E., Słota D., Ma’s identity and its applications, Annales Universitatis Paedagogicae Cracoviensis 2012, 11, 43-51.
• [12] Schuette P., A question of limits, Math. Magazine 2004, 77, 1, 61-68.