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Cauchy's formula

  • Thread starter sinned4789
  • Start date
  • #1

Homework Statement


specialize cauchy's formula to the case when z is the center of the circle and show that

f(z) = (1/2[tex]\pi[/tex])[tex]\int[/tex] f(z + re^(it)) dt
integral limits are 0 to 2[tex]\pi[/tex]


Homework Equations


cauchy's formula
f(z) = (1/i2*pi) [tex]\int[/tex] f([tex]\zeta[/tex])/([tex]\xi[/tex] - z) d[tex]\zeta[/tex]

it is 2*pi not 2^pi just to be sure


The Attempt at a Solution



i have no idea how to do this
any input or hints would be appreciated

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Just put zeta=z+r*e^(i*t). It's a simple substitution problem.
 

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