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    A series for sin az / sin pi z in complex analysis

    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...
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    Compact sets and homeomorphisms

    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...
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    Graphic calculators

    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.
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    Differential equation problem

    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...
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    Sinx and i

    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...
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    Solutions of matrices

    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...
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    Solving 3rd and 4th level equations

    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...
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    Proving Gregory's formula

    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} ... =...