Question

1. An electrostatic potential is given by: \begin{equation} V(r, \theta) = \frac{2.0}{r^{15}} f_{14}(cos(\theta)) \end{equation} where V is in Volts, $\theta$ is in radians, r is in meters, and $f_{14}(cos(\theta))$ is a function that can be calculated using the following recursive formula: \begin{equation} f_{n+1}(x) = \frac{(2n + 1)x f_n(x) - n f_{n-1}(x)}{n + 1} \end{equation} where $f_0(cos(\theta)) = 1$ and $f_1(cos(\theta)) = cos(\theta)$. For instance, to calculate $f_2(cos(\theta))$, you would set n = 1 and: \begin{equation} f_{1+1}(cos(\theta)) = \frac{(2 + 1) cos(\theta) f_1(cos(\theta)) - f_0(cos(\theta))}{2} \end{equation} Write two programs using the recursive formula (select two of the following lan- guages: C++, Python, FORTRAN), to calculate the value of the electric potential at $r = 0.82$ m and $\theta = \frac{\pi}{4}$ rad (10 points). Hint: Start by getting the numerical value of $f_0(cos(\theta))$ and $f_1(cos(\theta))$, then use the recursive formula to get $f_2, f_3, ... f_{14}$.

          1. An electrostatic potential is given by:
\begin{equation}
V(r, \theta) = \frac{2.0}{r^{15}} f_{14}(cos(\theta))
\end{equation}
where V is in Volts, $\theta$ is in radians, r is in meters, and $f_{14}(cos(\theta))$ is a function that
can be calculated using the following recursive formula:
\begin{equation}
f_{n+1}(x) = \frac{(2n + 1)x f_n(x) - n f_{n-1}(x)}{n + 1}
\end{equation}
where $f_0(cos(\theta)) = 1$ and $f_1(cos(\theta)) = cos(\theta)$. For instance, to calculate $f_2(cos(\theta))$,
you would set n = 1 and:
\begin{equation}
f_{1+1}(cos(\theta)) = \frac{(2 + 1) cos(\theta) f_1(cos(\theta)) - f_0(cos(\theta))}{2}
\end{equation}
Write two programs using the recursive formula (select two of the following lan-
guages: C++, Python, FORTRAN), to calculate the value of the electric potential
at $r = 0.82$ m and $\theta = \frac{\pi}{4}$ rad (10 points). Hint: Start by getting the numerical
value of $f_0(cos(\theta))$ and $f_1(cos(\theta))$, then use the recursive formula to get $f_2, f_3, ... f_{14}$.

1. An electrostatic potential is given by:

V(r, θ) = (2.0)/(r^15) f14(cos(θ))

where V is in Volts, θ is in radians, r is in meters, and f14(cos(θ)) is a function that
can be calculated using the following recursive formula:

fn+1(x) = ((2n + 1)x fn(x) - n fn-1(x))/(n + 1)

where f0(cos(θ)) = 1 and f1(cos(θ)) = cos(θ). For instance, to calculate f2(cos(θ)),
you would set n = 1 and:

f1+1(cos(θ)) = ((2 + 1) cos(θ) f1(cos(θ)) - f0(cos(θ)))/(2)

Write two programs using the recursive formula (select two of the following lan-
guages: C++, Python, FORTRAN), to calculate the value of the electric potential
at r = 0.82 m and θ = (π)/(4) rad (10 points). Hint: Start by getting the numerical
value of f0(cos(θ)) and f1(cos(θ)), then use the recursive formula to get f2, f3, ... f14.

Added by Chris J.

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