JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 4, Pages 349 - 362
(August 2016) http://dx.doi.org/10.17654/NT038040349 |
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SOLUTIONS OF THE CONNECTION PROBLEMS BETWEEN FERMAT AND GENERALIZED FIBONACCI POLYNOMIALS
W. M. Abd-Elhameed and Y. H. Youssri
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Abstract: This paper aims to develop innovative formulae linking Mersenne and Fermat numbers with a class of generalized Fibonacci numbers including the celebrated Fibonacci and Pell numbers. These formulae can be obtained by solving the connection problems between Fermat and generalized Fibonacci polynomials. The introduced connection formulae are obtained with the aid of the power from representations and inversion formulae of Fermat and generalized Fibonacci polynomials. We show that all the connection coefficients are expressed in terms of terminating hypergeometric functions of the type of certain arguments. |
Keywords and phrases: Fibonacci sequence, recurrence relation, hypergeometric functions, connection coefficients. |
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