Example: Bessel Functions of the First Kind
Show the relationship between functions J0, J1, and Jn. Also show the relationships between these functions and their scaled versions.
1. Define two step range variables:
2. Plot functions J0 and J1. Add the 2nd order function Jn to the plot:
3. Create a plot to show that J0(y)=Jn(0,y). Reset the tick mark values to zoom in the x-axis in order to show more details:
4. Create a plot to show that J1(y)=Jn(1,y). Reset the tick mark values to zoom in the x-axis in order to show more details:
5. Use symbolic evaluation to show the relationship between each Bessel function of the first kind and its scaled version:
6. Create a plot to show that:
J0.sc contains complex elements, so first apply the Re function to just show the real part of the numbers.
7. Calculate the coordinates of the first two peaks of J1. Use functions augment and localmax to identify the peaks that fall within the specified range:
Function localmax requires an input matrix of two columns. Function augment is used to create such a matrix.
8. Use function match to find the horizontal coordinates of the peaks. Reduce the value of TOL to get the most accurate results:
9. Add markers to the plot to mark the first two peaks:
The step range variable has a step of 0.1. This means that the peaks occur at 1/10 the element index identified by function match or 1.8 and 8.5 respectively.
