Question

Plot

1. ${\mathbf{l}}_{\mathbf{0}}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{,}\mathbf{}{\mathbf{l}}_{\mathbf{1}}\left(x\right)\mathbf{,}\mathbf{}{\mathbf{l}}_{\mathbf{2}}\left(x\right)$, from x = 0 to 2 .
2. ${\mathbf{K}}_{\mathbf{0}}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{,}\mathbf{}{\mathbf{K}}_{\mathbf{1}}\left(x\right)\mathbf{,}\mathbf{}{\mathbf{K}}_{\mathbf{2}}\left(x\right)$, from x = 0.1 to 2 .
3. role="math" localid="1659270507695" $\mathbf{Ai}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$from x = -10 to 10 .
4. role="math" localid="1659270512971" $\mathbf{Bi}\mathbf{\left(}\mathbf{x}\mathbf{\right)}$ from x = -10 to 1 .

Short answer

The figures show the behavior of Bessel functions of different kinds.

Step-by-step solution

Concept of Bessel functions:

The initial conditions that are given Analogous results about the behaviors of the Bessel functions of the second kind can be obtained.

The Bessel functions satisfy a large number of properties. The first two properties are easy to obtain from the series representation of ${\mathbf{J}}_{\mathbf{a}}$and the third has already been verified.

(a) Draw the graph and plot the points:

The graphs of ${\mathrm{J}}_0$and of ${\mathrm{J}}_1$resemble those of cosine and sine with a decreasing amplitude with respect to the zeros of localid="1659270840402" ${\mathrm{J}}_0$and ${\mathrm{J}}_1$ between two consecutive zeros of ${\mathrm{J}}_1$there is exactly one zero of ${\mathrm{J}}_1$.

(b) Draw the graph and plot the points:

Plot the graph as follows:

(c) Draw the graph and plot the points:

Plot the graph as follows:

(d) Draw the graph and plot the points:

Plot the graph as follows: