Q 24E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

Question:Use a CAS to graph  J_3/2(x),J_-3/2(x),J_5/2(x), and J_-5/2(x).

Step-by-Step Solution

Answer

The graph has been plotted.

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.

Step 2: Find the graph of j 3/2 (x) .

Use GNU Octave to plot the functions.

Step 3: Find the value of j - 3/2 (x) .

Let,

Step 4:Find the value of j 5 /2 (x) .

Let,

Step 5:Find the value of j -5/2 (x) .

Let,