- #1

timetraveller123

- 621

- 45

## Homework Statement

i have been trying to learn bessel function for some time now but to not much help

firstly, i don't even understand why frobenius method works why does adding a factor of x^r help to fix the singularity problem. i saw answers on google like as not all function can be represented like negative,fractional,complex exponents and adding the r helps to take of .

secondly, why does frobenius method only work when it is regular singular point. from what i saw

##

y'' + \frac{p(x)}{x}y' + \frac{q(x)}{x^2}y = 0

##

p and q need to analytic around zero why this condition. why wouldn't frobenius work if they weren't

thirdly, from what i see in the previous equation, for such equations the second derivative is not defined at zero. but when i see bessel function(solution of one such equation) the second derivative seems to be well defined at x =0

how is it not defined .

i am sorry if i don't make sense but i am very much a begineer in these thing it would be of much help if anyone could help me out thanks