I´m having a problem with the value of the expression
##F(it)-F(-it)##, found on the Abel-Plana formula, where $$F(z)=\sqrt{z^2 + A^2}$$, with ##A## being a positive real number (F(z) is analytic in the right half-plane).
Well, I know the result is ##F(it)-F(-it)=2i\sqrt{t^2 -A^2}##, for...
Sorry for not paying enough attention. Indeed, you have to choose something like Ax^2 +Bx (instead of Ax+B)as your particular solution, since you already have a constant as a solution from the homogenous equation.
Not exactly. Notice there's an \sqrt \alpha missing on the denominator.
Btw, I know the substitution simply by having done similar integrals many times over. Also, you can get the idea if you remember the usual trigonometric identities.
For integrals of the type
\int \frac{dx}{a^2 +x^2}, try the following substitution :
x=a \tan \theta
With a bit of algebra, you'll be able to put your integral at this form.
Homework Statement
I'd like some help with 2 problems:
Show by using Demoivre's theorem and the geometric series formula that the sum of all n values of z^(1/n) is zero when n >=2.
Z is a complex number.
Use the geometric series formula and Demoivre's theorem to show that:
Homework Equations...
Homework Statement
The problem is :''Resolve the cartesian unit vectors into their cylindrical components(using scale factors)
The Attempt at a Solution
It's simple to do the inverse(resolving cylindricl unit vectors into cartesian components),but I'm having some ''trouble'' with the...
Homework Statement
Hello,I'm having problems figuring out the solution of the following Integral.Any hints would be much appreciated!There it is:
I= sin(x)/sqrt{4sin(x)^2+cos(x)^2} dx
Here goes a theorem and its demonstration(attachment) .Sorry,I couldn't find it in english,so it's in portuguese).
We have that the intervals In=[An,Bn] which are closed and limited.
What I want to know is: what consideration(s) is/are NOT valid on the demonstration,when we consider an...