Bonnet's Recursion Formula using Spire for Polynomials... Legendre Polynomials

LegSpire.scala

def legendres(i: Int) : List[Polynomial[Rational]] = {
	val one = Polynomial(0 -> r"1/1")
	val x = Polynomial(1 -> r"1/1")
	lazy val leg : Stream[Polynomial[Rational]] = {
	  def loop(pnm1: Polynomial[Rational], pn: Polynomial[Rational], n: Int = 1) : Stream[Polynomial[Rational]] = {
	  	pn #:: loop(pn, Polynomial(0 -> Numeric[Rational].fromInt(n + 1).reciprocal) * (
	  				      (Polynomial(1 -> Numeric[Rational].fromInt(2 * n + 1)) * pn) + 
                  (Polynomial(0 -> Numeric[Rational].fromInt(n).unary_-) * pnm1)), n + 1)
	  }
	  one #:: loop(one, x)
	}
	leg.take(i).toList
}