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Magazine Problem 7
In Problems, find the Fourier series of \(f\) on the given interval.
$$
f(x)=x+\pi, \quad-\pi
Problem 8
Determine whether the function is even, odd, or neither.
$$
f(x)=\left\\{\begin{array}{lr}
x+5, & -2
Problem 8
(a) Find the eigenvalues and eigenfunctions of the boundaryvalue problem $$ y^{\prime \prime}+y^{\prime}+\lambda y=0, y(0)=0, y(2)=0 $$ (b) Put the differential equation in self-adjoint form. (c) Give an orthogonality relation.
Problem 8
Expand the given function in a FourierBessel series using Bessel functions of
the same order as in the indicated boundary condition.
$$
\begin{aligned}
&f(x)=x^{2}, 0
Problem 8
In Problems, find the Fourier series of \(f\) on the given interval.
$$
f(x)=3-2 x, \quad-\pi
Problem 8
Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set. $$ \\{\cos x, \cos 3 x, \cos 5 x, \ldots\\} ; \quad[0, \pi / 2] $$
Problem 9
Determine whether the function is even, odd, or neither. $$ f(x)=x^{3}, 0 \leq x \leq 2 $$
Problem 9
Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set. $$ \\{\sin n x\\}, n=1,2,3, \ldots ; \quad[0, \pi] $$
Problem 9
In Problems, find the Fourier series of \(f\) on the given interval.
$$
f(x)=\left\\{\begin{array}{lr}
0, & -\pi
Problem 10
Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set. $$ \left\\{\sin \frac{n \pi}{p} x\right\\}, n=1,2,3, \ldots ; \quad[0, p] $$
