# Is this a Bessel function?

1. Sep 15, 2011

### dfrenette

A nth order bessel function of the first kind is defined as:

Jn(B)=(1/2pi)*integral(exp(jBsin(x)-jnx))dx

where the integral limits are -pi to pi

I have an expression that is the exact same as above, but the limits are shifted by 90 degrees; from -pi/2 to 3pi/2

My question is how does this new expression relate to Bessel functions? My first thought was that the two function are equal since the integral limits are over one period. But I am not sure.

2. Sep 15, 2011

### edgepflow

I think they are different. I can not offer a mathematical proof, but using MathCAD function for Jn and its numerical integration, I obtained different numbers.

3. Sep 16, 2011

### JJacquelin

You are right. The two functions are equal.
A more tedious proof is given in the joint page :

#### Attached Files:

• ###### Bessel.JPG
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4. Sep 16, 2011

### dfrenette

Super,
Thanks for the proof!

I did set up a little mathcad file (attached) that shows the two implementations, proving to myself that indeed they are equal, but this proof will come in handy.

Where did you get it from so I can cite it?

Thanks again,

Darren

#### Attached Files:

• ###### BesselFunction.zip
File size:
50.4 KB
Views:
100
5. Sep 16, 2011

### edgepflow

Nice proof. I stand corrected.

The Bessel function I tried in MathCAD is: Jn(m, x) which returns Jm(x). Is this the same thing?

6. Sep 17, 2011

### JJacquelin

It's writen by myself. You can copy it. No need to cite an author : the calculus is rather classical.

7. Sep 19, 2011

### dfrenette

Perfect. Thanks again.