1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
2n-3 sequence 1st term
Alexandra [31]
First term = 2(1) - 3 = 2 - 3 = -1
8 0
3 years ago
Help my sister with this pls
NeX [460]

Answer:

23

Step-by-step explanation:

i think

3 0
3 years ago
Which multiplication equation can be used to solve 1/6 ÷ 5? ​
Anna [14]

Answer:

1/6 x 1/5 = multiplication equation

8 0
2 years ago
The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less t
Allushta [10]

Answer:

2 years

Step-by-step explanation:

13000 X 0.05 = 650    

13000 - 650 = 12350     year 1

12350 X 0.05 =617.5

12350 - 617.5 =11732.5     year 2

4 0
2 years ago
Please help and show wprk
mr Goodwill [35]
Volume of a cylinder is \pi r^2h, where r is the radius and h is the height.

This comes from the area of a circle being \pi r^2. A cylinder is the area of the base circle multiplied by its height.

Using this formula, the volume of the given cylinder is
\pi r^2(3r) \\
=  3 \pi r^3
6 0
3 years ago
Other questions:
  • The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraicall
    14·1 answer
  • I don't get # 2 please help and fast
    10·1 answer
  • Please answer it now in two minutes
    11·1 answer
  • Explain the difference between discrete and continuous
    14·1 answer
  • What is the numeral preceding 100000 with base of 4​
    5·1 answer
  • What is y=-6x-8 in standard form
    8·2 answers
  • Does this table represent a proportional relationship?<br><br> Yes<br> No
    5·1 answer
  • Freeee points bc iz the hoidays booooooi ​
    15·2 answers
  • Reflect (8,9) across the x-axis. Then reflect the result across the y-axis. What are the coordinates of the final point?​
    8·1 answer
  • I will mark you brainiest if you can answer this
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!