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Reseach Article

Certain Combinatorial Identities of Twin Pairs Related to Tchebychev Polynomials

by R. Rangarajan, Shashikala P., Honnegowda C. K.
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 154 - Number 5
Year of Publication: 2016
Authors: R. Rangarajan, Shashikala P., Honnegowda C. K.
10.5120/ijca2016912132

R. Rangarajan, Shashikala P., Honnegowda C. K. . Certain Combinatorial Identities of Twin Pairs Related to Tchebychev Polynomials. International Journal of Computer Applications. 154, 5 ( Nov 2016), 1-5. DOI=10.5120/ijca2016912132

@article{ 10.5120/ijca2016912132,
author = { R. Rangarajan, Shashikala P., Honnegowda C. K. },
title = { Certain Combinatorial Identities of Twin Pairs Related to Tchebychev Polynomials },
journal = { International Journal of Computer Applications },
issue_date = { Nov 2016 },
volume = { 154 },
number = { 5 },
month = { Nov },
year = { 2016 },
issn = { 0975-8887 },
pages = { 1-5 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume154/number5/26484-2016912132/ },
doi = { 10.5120/ijca2016912132 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:00:02.345922+05:30
%A R. Rangarajan
%A Shashikala P.
%A Honnegowda C. K.
%T Certain Combinatorial Identities of Twin Pairs Related to Tchebychev Polynomials
%J International Journal of Computer Applications
%@ 0975-8887
%V 154
%N 5
%P 1-5
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In the present paper, a twin pair (xn, yn) and (Xn, Yn) of numbers related to one and two variable Tchebychev polynomials of first and second kinds are proposed. Certain Combinatorial Identities of the twin pairs are stated and proved.

References
  1. W. S. Anglin, The Queen of Mathematics, An Introduction to Number Theory, Kluwer Academy Publishers, 1995.
  2. D. M. Burton, Elementary Number Theory, Wm.C.Brown Company Publisher,1989 .
  3. W. Gautschi, Orthogonal Polynomials: Computation and Approximation, Oxford University Press, New York, 2004.
  4. R. L. Graham, D. E. Kunth and O. Patashnik, Concrete Mathematics Second Edition, Pearson Education Inc., 1994.
  5. G. H. Hardy and E. M. Wright, An Introduction to Theory of Numbers, Clarendon Press, 1979.
  6. J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, CRC Press LLC, New York, 2003.
  7. J. Morgado, Note on the Chebyshev Polynomials and Applications to the Fibonacci Number, Portugaliae Mathematica, 52(1995), 363-378.
  8. R. Rangarajan and P. Shashikala, A Pair of Clasical Orthogonal Polynomials Connected to Catalan Numbers, Adv Studies Contemp.Math., 23(2013), 323-335 .
  9. E.D. Rainville, Special Functions, The Macmillan company, New york, 1960.
  10. J. Riordan, Combinatorial Identities, Robert E. Krieger Publishing Company, New York, 1979.
  11. T. Rivlin, Chebyshev Polynomials : From Approximation Theory to Number Theory, Second edition, Wiley and Sons, New York, 1990.
  12. P. Shashikala, Studies on mathematical analysis of orthogonal polynomials, Ph. D. Thesis, University of Mysore, Mysore, 2014.
  13. P. Shashikala and R. Rangarajan, Tchebychev and Brahmagupta Polynomials and Golden Ratio:Two New Interconections, International J.Math. Combin., 3(2016), 57-67.
  14. H. M. Stark, An Introduction to Number Theory, Cambridge MIT Press, New York, 1994.
  15. S. Vajda, Fibonacci and Lucas Numbers and Golden Section, Theory and Applications, Ellis-Horwood, London, 1989.
Index Terms

Computer Science
Information Sciences

Keywords

Combinatorial Identities Continued fractions and Functions of hypergeometric type in one and severable variables