Starting from the generating function of the Legendre polynomial, prove that P,(1)=1 and Pr(-x)=(-1)^Pn(x).

Example of numerical instability: Take y′ = −5y, y(0) = 1. We know that the solution should decay to zero as x grows. Using Euler’s method, start with h= 1 and compute y1, y2, y3, y4 to try to approximate y(4). What happened? Now halve the interval. Keep halving the interval and approximating y(4) until the numbers you are getting start to stabilize (that is, until they start going towards zero).

Please help

Evaluate the commutator è = [x², Pe** =?