1).The Bessel functions Jp satisfy the equations (see attached file) . Use this to show that Bessel functions satisfy Bessel's differential equation. 2) The legendre polynomials satisfy... (see attached) where Pn(x) is the Legendre polynomial of degree n. Show that the Legendre satisfy Legendre's differential equation, (see attached)© BrainMass Inc. brainmass.com October 5, 2022, 6:17 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
The solution is attached.
Taking equation 2 with p-1 gives
Taking the derivative of equation 1 gives
Comparing the right hand sides,
Rearranging, we see that
Thus the Bessel Functions solve Bessel's equation.
Taking the derivative of equation 4,
From equation 3, we see that . Substituting this in gives
Thus the Legendre polynomials satisfy Legendre's equation.© BrainMass Inc. brainmass.com October 5, 2022, 6:17 pm ad1c9bdddf>