let be a sequence of polynomials of real variable defined by
show that for all
and then show that converges uniformly to
i need help, i tried to do the first part by induction but i dont seem to get to something useful
let be a sequence of polynomials of real variable defined by
show that for all
and then show that converges uniformly to
i need help, i tried to do the first part by induction but i dont seem to get to something useful
The 'attack procedure' used in...
http://www.mathhelpforum.com/math-he...nvergence.html
... works succesfully also in this case...
The equation generating the sequence of functions can be written as...
(1)
The is represented here...
The only 'attractive fixed point' is the positive zero of the equation that is...
(2)
... so that if converges, it does converge to . The condition for convergence is , where is the 'red line' crossing the axis in with slope equal to and in this case is...
(3)
... which is satisfied for...
(4)
Kind regards