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Nookie1986 [14]
3 years ago
7

Analytic function on unit disk with power series has pole on unit circle, then power series diverges on unit circle.

Mathematics
1 answer:
Wittaler [7]3 years ago
8 0

Answer:

The function

{\ displaystyle f (z) = {\ frac {z} {1- | z | ^ {2}}}} {\ displaystyle f (z) = {\ frac {z} {1- | z | 2}

It is an example of real and bijective analytical function from the open drive disk to the Euclidean plane, its inverse is also an analytical function. Considered as a real two-dimensional analytical variety, the open drive disk is therefore isomorphic to the complete plane. In particular, the open drive disk is homeomorphic to the complete plan.

However, there is no bijective compliant application between the drive disk and the plane. Considered as the Riemann surface, the drive disk is therefore different from the complex plane.

There are bijective conforming applications between the open disk drive and the upper semiplane and therefore determined as Riemann surfaces, are isomorphic (in fact "biholomorphic" or "conformingly equivalent"). Much more in general, Riemann's theorem on applications states that the entire open set and simply connection of the complex plane that is different from the whole complex plane admits a bijective compliant application with the open drive disk. A bijective compliant application between the drive disk and the upper half plane is the Möbius transformation:

{\ displaystyle g (z) = i {\ frac {1 + z} {1-z}}} {\ displaystyle g (z) = i {\ frac {1 + z} {1-z}}}

which is the inverse of the transformation of Cayley.

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Which answer is it I’m doing my quiz rn
anyanavicka [17]

Answer:

10

Step-by-step explanation

3 x 4 = 12

8 + 12 = 20

20 / 2 = 10

8 0
3 years ago
Read 2 more answers
HELP:
wel

Answer:

First you can find the rate of change to be 4.25. Then you can subtract 4.25 repeatedly until you get to an output with an input of zero. The initial value is the output when the input is zero. The initial value after subtracting 4.25 three times is 29.50. Because the inputs go by 2, the rate of change is half the difference of the outputs, or 4.25. Subtract 4.25 repeatedly 3 times to get to an output with an input of 0. Calculate 42.25 – (3 x 4.25).  The initial value is 29.50.

Hope this Helps!

6 0
2 years ago
If f (x) = x + 7 and g (x) = StartFraction 1 Over x minus 13 EndFraction, what is the domain of (f circle g) (x)?
Rashid [163]

Answer:

R-{13}

Step-by-step explanation:

We are given that

f(x)=x+7

g(x)=\frac{1}{x-13}

We have to find the domain of fog(x).

fog(x)=f(g(x))

fog(x)=f(\frac{1}{x-13})

fog(x)=\frac{1}{x-13}+7=\frac{1+7x-91}{x-13}=\frac{7x-90}{x-13}

Domain of f(x)=R

Because it is linear function.

Domain of g(x)=R-{13}

Because the g(x) is not defined at x=13

fog(x) is not defined at x=13

Therefore, domain of fog(x)=R-{13}

6 0
3 years ago
Read 2 more answers
Which table represents a linear function?
Delvig [45]

Answer:

I would go with the first one.

Step-by-step explanation:

The first one is the only one that increases by the same number. In other words, its slope is constant. A linear function has a constant slope. You can tell that it increases by 1/2 every time.

6 0
3 years ago
Solve for x. <br> y=bx+a<br><br> please hurry
ivann1987 [24]

I believe the solution is x=\frac{y-a}{b}.

I hope this helped you out!

6 0
3 years ago
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