When studying a polynomial, it is sometimes useful to have an explicit representation for the polynomial that makes it clear one has a polynomial. Surprisingly, there are polynomials defined by three term recurrence relations for which explicit formulas exist, yet the formulas do not make it clear that the functions are polynomials. Important examples are the associated Pollaczek polynomials, which satisfy \(p_{- 1}(x)=0\), \(p_ 0(x)=1\), and \[ (n+c+1)p_{n+1}(x)+(n+2\lambda +c- 1)p_{n-1}(x)=2[(n+\lambda +a+c)x+b]p_ n(x). \] The known representations are as quotients of 2 by 2 determinants of hypergeometric functions. The case \(c=0\) is special, and here there is a hypergeometric representation where the polynomial character can be shown. For the general case a relatively nice formula as a double series is found in this paper. Now is it clear that the polynomials are polynomials in x and \((1-x^ 2)^{1/2}\), yet it is not clear they are polynomials in x. Some very interesting limit cases are stated explicitly. Some explicit Padé approximations are given.