New Generalizations of Fibonacci and Lucas Polynomials

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Poonchayar Patthanangkoor
Chonticha Chinsaard
Wisinee Ngamsriwiset
Thofun Waewkrathok

Abstract

We consider the polynomials fn(x)  and ln(x)   which are generated by the recurrence relations fn(x) = 2ax fn-1(x)+(b-a2) fn-2(x)   for n >=2  and ln(x) = 2ax ln-1(x)+(b-a2) ln-2(x)  for n >=2 with the initial conditions f0(x) =0 , f1(x) =1 and  l0(x) =2 , l1(x) =2ax  where  a and  b are any non-zero real numbers. We obtain the new generalizations of Fibonacci and Lucas polynomials. Moreover, we obtain generating functions, Binet’s formulas and some identities involving  fn(x)  and ln(x) .

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