gistfile1.cs

delegate Func<T1, T2> Recursive<T1, T2>(Recursive<T1, T2> r);

public static Func<T1, T2> Y<T1, T2>(Func<Func<T1, T2>, Func<T1, T2>> f)
{
    return ((Recursive<T1, T2>)(g => n => f(g(g))(n)))(
                                g => n => f(g(g))(n));
}

gistfile2.cs

var fact = Y<int, int>(partial => n => n == 0 ? 1 : n * partial(n - 1));
Console.WriteLine(fact(5)); // Prints 120