Fibonacci Polynomial Calculator

F_{n+1}(x) = xF_n(x)+F_{n-1}(x)

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F_8(1)

L_8(1)

x=1 → Fibonacci numbers!

Sequence at x=1

n=1F=1L=1

n=2F=1L=3

n=3F=2L=4

n=4F=3L=7

n=5F=5L=11

n=6F=8L=18

n=7F=13L=29

n=8F=21L=47

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About Fibonacci Polynomial Calculator

A Fibonacci polynomial calculator computing F_n(x) with F_1=1, F_2=x, F_{n+1}=xF_n+F_{n-1} and Lucas polynomials L_n(x) with L_1=x, L_2=x²+2. At x=1: F_n(1)=Fibonacci numbers. Connections to Chebyshev polynomials and continued fractions. Client-side.

Fibonacci Polynomial Calculator Features

F_n(x) value
L_n(x) value
Coefficients
Special values
Sequence

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