Recent content by LagrangeEuler

Yes, I know that. But I do not know how to find those examples.

Yes and I did not find any other example.

Can you give me two more examples for essential singularity except f(z)=e^{\frac{1}{z}}? And also a book where I can find those examples?

After all this time I feel that I do not have an answer for the same question. Can someone propose me a book where I can read something about it? Because from the graph of the gamma function, it looks like #\Gamma(-2)## is not defined. Also #\lim_{x \to -2^{+}}=\infty# and #\lim_{x \to...

Why? Eigenvalue can be for instance ##i##.

No, because the identity matrix is diagonal.

You can give me 2x2 example. But specify ##A##, ##U## and ##D##. Because ##U## still possibly can be formed of eigenvectors of ##A## in your example of ##U##.

Yes here I am talking about case ##U=U^{-1}##. I am also not sure. But for me it is interesting.

Every hermitian matrix is unitary diagonalizable. My question is it possible in some particular case to take hermitian matrix ##A## that is not diagonal and diagonalize it UAU=D but if ##U## is not matrix that consists of eigenvectors of matrix ##A##. ##D## is diagonal matrix.

Can you please explain this series f(x+\alpha)=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^nf}{dx^n} I am confused. Around which point is this Taylor series?

##y''(t)+\sin(t)y(t)=0##, where ##y(0)=A##, ##y'(0)=B##. If I apply the Laplace transform would I get the differential equation of infinite order?

I do not understand why ##(Z.+)## is the cyclic group? What is a generator of ##(Z,+)##? If I take ##<1>## I will get all positive integers. If I take ##<-1>## I will get all negative integers. I should have one element which generates the whole group. What element is this?

It is only in the case when you have a differential equation with constant coefficients.

Is it possible to apply Laplace transform to some equation of finite order, second for instance, and get the differential equation of infinite order?

If we have two functions ##f(x)## such that ##\lim_{x \to \infty}f(x)=0## and ##g(x)=\sin x## for which ##\lim_{x \to \infty}g(x)## does not exist. Can you send me the Theorem and book where it is clearly written that \lim_{x \to \infty}f(x)g(x)=0 I found that only for sequences, but it should...