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**Kevin_Jiang****Member**- Registered: 2005-10-23
- Posts: 3

A Bessel function (of the first kind, I mean here) can nowdays be routinely calculated if given the order of the Bessel function. Bessel Function plots are also known corresponding to specific orders. Pls visit

http://www.phys.ufl.edu/~dorsey/phys6346/worksheets/bessel1.html for examples.

My question is: If I were given a plot of some Bessel function without known its order, how could I retrieve the order of the Bessel Function from the plot? Please note that the absolute x-coordinate is missing from the plot, i.e. we cannot read out the absolute x-values for those Bessel zeros.

Thanks in advance. I appreciate your help.

email: kevin_21cn@lycos.com

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

I know nothing about Bessel functions, but I went to the address you gave, and the three graphs shown there all look different--they all intersect the y-axis in different spots. Are they all different orders? Perhaps you could tell them apart in this way - by their y intercept.

El que pega primero pega dos veces.

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**Kevin_Jiang****Member**- Registered: 2005-10-23
- Posts: 3

Thank you, ryos. You are right, the zero-order Bessel function can be easily identified because it has intercept on y-axis at 1. However, all other Bessel functions intersect the y-axis at zero. The problem is how to recognize those higher-order Bessel functions?

Looking forward to any possible solution. Thanks.

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

The second two graphs on the page you linked are subtly different. One begins concave-upward, the other downward. I'm betting you could guess it from the slope of a tangent line near 0.

Again, I know nothing about bessel functions.

El que pega primero pega dos veces.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

It looks like a graph of dampened harmonic motion - a sinusoidal wave whose amplitude is constantly changing subject to an exponential decay - but it might just be something similar.

I also know nothing about bessel functions

Why did the vector cross the road?

It wanted to be normal.

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**Kevin_Jiang****Member**- Registered: 2005-10-23
- Posts: 3

The wabpage that I refered to gives just a very few samples. In practice, I have measurements that could be described as Bessel functions of all possible kinds of orders from 0 to 40 around. My problem is how to retreive exactly the order of the corresponding Bessel function.

More examples can be found at

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

Is Bessel function a "cold" topic in Math World?

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