Palindromic polynomial

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A polynomial is palindromic, if the sequence of its coefficients are a palindrome.

Let be a polynomial of degree n, then P is palindromic if a_i = a_{n − i} for i=0...n.

Similarly, P is called antipalindromic if a_i = − a_{n − i} for i=0...n.

[edit] Examples

Some examples of palindromic polynomials are:

(x + 1)² = x² + 2x + 1

(x + 1)³ = x³ + 3x² + 3x + 1

Generally, the expansion of (x + 1)ⁿ is palindromic for all n (can see this from binomial expansion)

It also follows that if P is of even degree (so has odd number of terms in the polynomial), then it can only be antipalindromic when the 'middle' term is 0, i.e. a_i = − a_i, where n = 2i.

[edit] See also

• Reciprocal polynomial

[edit] External links

• MathPages - The Fundamental Theorem for Palindromic Polynomials