Question

Question:Use a CAS to graphJ_3/2(x),J_-3/2(x),J_5/2(x), and J_-5/2(x).

Short answer

The graph has been plotted.

Step-by-step solution

Step 1:Define Spherical Bessel’s equation.

Bessel functions of half-integral order are used to dene two more important functions:

$j_n\left(x\right)=\sqrt{\frac{\mathrm{\pi }}{2x}}{J}_{n+1/2}\left(x\right)$

$y_n\left(x\right)=\sqrt{\frac{\mathrm{\pi }}{2x}{Y}_{n+1/2}}\left(x\right)$

The function j_n (x)is called the spherical Bessel function of the first kind and y_n (x) is the spherical Bessel function of the second kind.

Find the graph of j3/2 (x) .

Use GNU Octave to plot the functions.

Find the value of j-3/2(x) .

Let,

Step 4:Find the value of j5/2 (x) .

Let,

Step 5:Find the value of j-5/2 (x) .

Let,