Recent content by Big-T

How about letting x^x = e^{x\ln x} ?

http://www.sosmath.com/calculus/integration/fant/fant.html

How would one go about to construct a function on (smooth) manifolds that is a submersion without being (the projection map of) a fiber bundle?

What contour have you used? Could it have something to with the choice of brance of the square root function?

For the two last posts, isn't it supposed to be (y - 1/y)/2i = 2i ?

Imagine the unit circle projected onto the y-axis, then pi/4 corresponds to 1, 0 and pi to 0 and -pi/4 to -1 as initial positions.

Your initial conditions gives these equations, from which you should be able to retrieve u: r(t)=Asin(wt+u) r(0)=A

Marcus' function would be well defined if we agreed to use trailing nines wherever the decimal expansion is terminating, this should of course have been specified.

How many basis vectors do you need to span P_k?

How could that possibly be a bijection? Obviously, z_1=a+ib is mapped to the same point as z_2=a z_1, so it is not an injection. Marcus has already provided a valid bijection, his "decimal merging" is the classical example of this. Notice how it is also valid in \mathbb{R}^n.

What RedBranchKnight refers to is a special case of the http://en.wikipedia.org/wiki/Method_of_characteristics" .

Rudin defines pi/2 to be the smallest positive number such that cos(pi/2)=0.

You may have a look here: http://en.wikipedia.org/wiki/Inverse_trigonometric_function#Logarithmic_forms"

That definition put everything in place, thanks!

I.e. the multiplicity is the power of the term with the largest negative power in the laurent series of the function? Does this also mean that an isolated/(essential?) singularity is a pole with infinite multiplicity?