Palindromic polynomial
Encyclopedia
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 
for i=0...n.
Similarly, P is called antipalindromic if
for i=0...n.
Generally, the expansion of
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.
, where 
.
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
is palindromic, if the sequence of its coefficients are a palindrome
Palindrome
A palindrome is a word, phrase, number, or other sequence of units that can be read the same way in either direction, with general allowances for adjustments to punctuation and word dividers....
.
Let
be a polynomial of degree n, then P is palindromic if for i=0...n.Similarly, P is called antipalindromic if
for i=0...n.Examples
Some examples of palindromic polynomials are:Generally, the expansion of
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.
, where .