## Bessel's Equation Solution Proof

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 .
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 Recognitions: Gold Member Science Advisor Staff Emeritus "Proving a function" is nonsensical -- what are you trying to ask?
 Blog Entries: 9 Recognitions: Homework Help Science Advisor There you go http://mathworld.wolfram.com/BesselF...FirstKind.html and the links for the rest of the treatment... Daniel.

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## Bessel's Equation Solution Proof

You may wanna chack this thread,too.

Daniel.

 Quote by Hurkyl "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) .
 Blog Entries: 9 Recognitions: Homework Help Science Advisor U mean how to get the Bessel ODE starting from where? Daniel.

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 Quote by hi_mostafa 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.

 Quote by 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.
exactly , as you said ,

any one help .
 Recognitions: Gold Member Homework Help Science Advisor 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.
 Recognitions: Gold Member Science Advisor Staff Emeritus 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.
 yes , but i don't know how to write latex .
 Blog Entries: 9 Recognitions: Homework Help Science Advisor If u're gonna keep posting math/physics related subjects here,please learn LaTex,it's not difficult. Daniel.
 Hi friends, I am struggling on the concepts of fourier integral transforms. Anyone who knew can sent to me. thanks
 erwin kreziog advanced engineering mathematics book is very nice
 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.

 Quote by dvs77 erwin kreziog advanced engineering mathematics book is very nice

I found this book online. Author is Erwin Kreysig.
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...