Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2005-10-24 02:09:10

Kevin_Jiang
Novice

Offline

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.

email:  kevin_21cn@lycos.com

## #2 2005-10-24 12:42:52

ryos
Power Member

Offline

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
Novice

Offline

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
Power Member

Offline

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
Moderator

Offline

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.

Kevin_Jiang
Novice

Offline