View Single Post
mmwave
#1
Nov2-03, 11:27 PM
P: 211
I've done a power series solution to a differential equation and got the recursive formula for the coefficients below. Now I am to evaluate it for large j and I don't get the answer in the book.

I'm not sure what method they are using to get the answer although their answer makes sense physically.

a j+1 = aj * 2 * {(j + L + 1) - k }/ ( {j+1}(j + 2L + 2) )

where L and k are constants and j is just an integer index number.

If I consider large j I would say
aj+1 approx. aj * 2 (j) / ( j * j) = aj * 2/j

If I say j => infinity and use l'Hopital's rule I get

aj+1 = aj * 2 / (2j + 2L + 3) approx. aj * 1/j

The book gets

aj+1 approx. aj * 2j / ( j*(j+1))

What rules are they applying to get this?

(of course a j+1 means aj+1 and aj means aj )
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history