Bessel's Equation Solution Proof

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In summary, Daniel is asking for help in proving a function, starting from the differential equation. He has found a book online that may help, but he is not sure how to write the equations in latex. He also recommends another book, by the same author, that provides more details on how to solve the Bessel ODE.
  • #1
hi_mostafa
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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 .
 
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  • #2
"Proving a function" is nonsensical -- what are you trying to ask?
 
  • #5
Hurkyl said:
"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) .
 
  • #6
U mean how to get the Bessel ODE starting from where?

Daniel.
 
  • #7
hi_mostafa said:
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.
 
  • #8
saltydog said:
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 .
 
  • #9
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
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
yes , but i don't know how to write latex .
 
  • #12
If u're going to keep posting math/physics related subjects here,please learn LaTex,it's not difficult.

Daniel.
 
  • #13
start with power series y=x^m(sigma an x^n)
 
  • #14
Hi friends,
I am struggling on the concepts of Fourier integral transforms.
Anyone who knew can sent to me.
thanks
 
  • #15
erwin kreziog advanced engineering mathematics book is very nice
 
  • #16
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
dvs77 said:
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
 
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Related to Bessel's Equation Solution Proof

1. What is Bessel's equation?

Bessel's equation is a type of differential equation that is used to describe various physical phenomena, such as heat flow and wave propagation.

2. What is the solution to Bessel's equation?

The solution to Bessel's equation is a set of functions known as Bessel functions. These functions are used to solve problems involving cylindrical and spherical coordinates.

3. How is Bessel's equation solved?

Bessel's equation can be solved using various methods, such as power series, Frobenius method, and the Laplace transform. These methods involve manipulating the equation to find a solution that satisfies the initial conditions.

4. How is the proof of Bessel's equation solution significant?

The proof of Bessel's equation solution is significant because it provides a mathematical foundation for solving a wide range of problems in physics and engineering. It also demonstrates the power and versatility of mathematics in describing and predicting natural phenomena.

5. Are there any practical applications of Bessel's equation solution?

Yes, there are many practical applications of Bessel's equation solution. For example, Bessel functions are used in solving problems related to heat transfer, vibration analysis, and electromagnetic wave propagation. They are also used in the design and analysis of various mechanical and electrical systems.

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