How to solve Differential equation

[giorgio_29]

Hello!
How to solve this diff eq?

$$\ y'' + a$$$$\frac {y} {x}$$ $$\ +b$$$$\frac {y} {x^2}$$ $$\ = 0$$

 

[giorgio_29]

Malmstén?

 

[AiRAVATA]

ANSAT:

$$y(x)=\sum_{n=0}^\infty a_n x^n$$

 

[giorgio_29]

yes Frobenius series for fuchsian points..., but Malmstén found the solution in term of modified Bessel functions, it is quite better.

 

[AiRAVATA]

Then you need to transform such equation to look like the modified Bessel equation.

 

[giorgio_29]

yes yes

the transformations are in the Watson book

the equation transform into a Bessel equation by using Malmstén transformations.

 

[AiRAVATA]

Then what is the question?

 

[giorgio_29]

after asking how to solve that equation I found the solution.

tks

gio