Bessel's Equation Solution Proof

1. Apr 17, 2005

hi_mostafa

hi there ,

i need the proof of the j(x) function starting from Bessel's Differential Equation .

and if anyone has any Online free book , or research on Bessel for first , second and Hankel in DETAILS , plz tell me about it .

Thanks .

2. Apr 17, 2005

Hurkyl

Staff Emeritus
"Proving a function" is nonsensical -- what are you trying to ask?

3. Apr 17, 2005

dextercioby

4. Apr 17, 2005

dextercioby

5. Apr 17, 2005

hi_mostafa

I mean the derivation of the Differential bessel equation
in order to end with J(x) .

6. Apr 17, 2005

dextercioby

U mean how to get the Bessel ODE starting from where?

Daniel.

7. Apr 17, 2005

saltydog

I think you mean: starting with Bessel's ODE, and using power series, and all of the tough work adjusting the series to look like the Bessel functions.

8. Apr 18, 2005

hi_mostafa

exactly , as you said ,

any one help .

9. Apr 18, 2005

arildno

hi, mostafa:
Start with posting the differential equation, and show what you have done so far (preferably in the LATEX format).

There are plenty of us who know how this should be done, but it is forum policy (and beneficial to yourself) that you do most on your own, and that we help you at those particular places you're stuck.

10. Apr 18, 2005

HallsofIvy

Actually, J(x) (more generally Jn(x)]) is defined as the solution to Bessel's equation. That J(x) is a certain power series could be proven using Frobenius' method.

11. Apr 18, 2005

hi_mostafa

yes , but i don't know how to write latex .

12. Apr 18, 2005

dextercioby

If u're gonna keep posting math/physics related subjects here,please learn LaTex,it's not difficult.

Daniel.

13. Apr 19, 2005

dvs77

14. Apr 19, 2005

sreekanth

Hi friends,
I am struggling on the concepts of fourier integral transforms.
Anyone who knew can sent to me.
thanks

15. Apr 20, 2005

dvs77

erwin kreziog advanced engineering mathematics book is very nice

16. Oct 6, 2009

vjraghavan

Another book that discusses neatly the Bessel ODE is Differential Equations by Lomen and Mark. It gives all basic details, definitions and theorems (without proofs) that are required to solve the problem. This book assumes that you have already done a basic course in Calculus are comfortable with concepts on Sequences and Series.

17. Jun 29, 2011

rajsodhi

I found this book online. Author is Erwin Kreysig.