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#1 2005-10-24 02:09:10
- Kevin_Jiang
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Please help me on Bessel Function
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
#2 2005-10-24 12:42:52
- ryos
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Re: Please help me on Bessel Function
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.
#3 2005-10-25 04:45:04
- Kevin_Jiang
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Re: Please help me on Bessel Function
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.
#4 2005-10-25 05:03:36
- ryos
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Re: Please help me on Bessel Function
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.
#5 2005-10-25 05:12:47
- mathsyperson
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Re: Please help me on Bessel Function
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.
#6 2005-10-25 16:32:19
- Kevin_Jiang
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Re: Please help me on Bessel Function
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?