Homework Statement
Show that
\frac{\sin (az)}{\sin (\pi z)} = \frac{2}{\pi} \sum_{n=1}^{+\infty} (-1)^n \frac{n \sin (an)}{z^2 - n^2}
for all a such that - \pi < a < \pi
Homework Equations
None really, we have similar expansions for \pi cot (\pi z) and \pi / \sin (\pi z) , this...
Hi there.
I'm taking a course in analysis and I was thinking about the relation between compact sets and homeomorphism. We know that if f is an onto and one-to-one homeomorphism then it follows that for every subset K:
K is compact in M <=> f(K) is compact in N
Now, does this go the...
I'm starting university to learn mathematics and I'm looking for a good graphical calculator, what are good value-for-money models that would be useful for some time to come?
Thanks,
Gunnar.
The last example on my homework assignment this week is this: Solve the following differential equation.
y'' + 2y' + y = e^{-x}
I started by solving it like it was y'' + 2y' +y = 0 (Instert y = e^ax and so on) and got the following equation and solution:
e^{ax}(a^2 + 2a + 1) = 0 => a...
Quick question.
sin(-x) = -sin(x)
this can be seen as this example:
sin(i^2x) = i^2sin(x)
Does this then apply?
sin(ix) = isin(x) ?
I'm trying to derive a formula for the length of a simple parabola. Unfortunetly in my calculations I end up with Arcsin(i2x) along the way and it...
I'm trying to learn linear algebra by myself from a book called "Introduction to linear algebra" by A.D. Martin and V.J. Mizel. One point I'm so far pretty confused about is whether a matix has a solution only if m equals n? I think the book says that if m < n the matrix has infinite solutions...
I think one of my books mentioned a way of solving third level equations (ax^3 + bx^2 + cx + d) and fourth level equations (Same as before, add nx^4) much the same way as you do with second level equations ((-B +- Sqrt(B^2 - 4AC))/2A). I have two questions, do you guys know the formulas for...
Hello,
I was talking to a friend of mine that's studying math at the university here and he gave me this problem to solve: Prove Gregory's formula. I'm going nuts. I've broken it down into a single sum like this:
\frac{\pi}{4} = 1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7} ... =...