I have recursive polynomials

$$Q_{n}(t)=tQ_{n-1}(t)+\frac{1-t^{2}}{n+1}Q'_{n-1}(t)$$

and

$$Q_{0}(t)=1$$

Is there a theory for finding a factorisation of recursive polynomials?

It is possible to show that $$\sum_{s}sinc(\pi(x+s))^{p+1}=Q_{p-1}[cos(\pi x)]$$

Maybe you have some ideas for my case?

I have recursive polynomials

$$Q_{n}(t)=tQ_{n-1}(t)+\frac{1-t^{2}}{n+1}Q'_{n-1}(t)$$

and

$$Q_{0}(t)=1$$

Is there a theory for finding a factorisation of recursive polynomials?

It is possible to show that $$\sum_{s=-\infty}^{\infty}sinc(\pi(x+s))^{p+1}=Q_{p-1}[cos(\pi x)]$$ where $$sinc(x)=sin(x)/x$$

Maybe you have some ideas for my case?

I have recursive polynomials  $$Q_{n}(t)=tQ_{n-1}(t)+\frac{1-t^{2}}{n+1}Q'_{n-1}(t)$$ and  $$Q_{0}(t)=1$$

Is there a theory for finding a factorisation of recursive polynomials?

It is possible to show that $$\sum_{s}sinc(\pi(x+s))^{p+1}=Q_{p-1}[cos(\pi x)]$$

Maybe you have some ideas for my case?

I have recursive polynomials 

$$Q_{n}(t)=tQ_{n-1}(t)+\frac{1-t^{2}}{n+1}Q'_{n-1}(t)$$ 

and 

$$Q_{0}(t)=1$$

Is there a theory for finding a factorisation of recursive polynomials?

It is possible to show that $$\sum_{s}sinc(\pi(x+s))^{p+1}=Q_{p-1}[cos(\pi x)]$$

Maybe you have some ideas for my case?