Bessel's Equation Solution Proof

[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 , please tell me about it .

Thanks .

 

[Hurkyl]

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

 

[dextercioby]

There you go

http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html

and the links for the rest of the treatment...

Daniel.

 

[dextercioby]

You may want to chack this thread,too.

https://www.physicsforums.com/showthread.php?t=69444

Daniel.

 

[hi_mostafa]

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

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

 

[dextercioby]

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

Daniel.

 

[saltydog]

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

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.

 

[hi_mostafa]

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.

exactly , as you said ,

any one help .

 

[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.

 

[HallsofIvy]

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

 

[hi_mostafa]

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

 

[dextercioby]

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

Daniel.

 

[dvs77]

start with power series y=x^m(sigma an x^n)

 

[sreekanth]

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

 

[dvs77]

erwin kreziog advanced engineering mathematics book is very nice

 

[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.

 

[rajsodhi]

erwin kreziog advanced engineering mathematics book is very nice

I had the same question...

I found this book online. Author is Erwin Kreysig.
Adavanced Engineering Mathematics. page 182.
Nice book! Thanks for the tip.

Wikipedia doesn't give any derivation.
Mathworld gives some more color but it's still rather foggy.
There's a soundless video on YouTube that explains a little more...


Yours,

Raj