Notation of branch cut of logarithm

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Just a small question on the notation of showing how the branch cut is chosen:




$log(z-c)$ is defined as $arg(z-c)in[theta_0,theta_0+2pi)$ with straight branch cut.




VS




$log(z-c)$ is defined as having a branch cut from $c$ to $infty e^itheta_0$.




Does both statements unambiguously define the branch cut of the function? If yes, which statement is more common/generally accepted?




complex-analysis soft-question




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    up vote
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    down vote

    favorite












    Just a small question on the notation of showing how the branch cut is chosen:




    $log(z-c)$ is defined as $arg(z-c)in[theta_0,theta_0+2pi)$ with straight branch cut.




    VS




    $log(z-c)$ is defined as having a branch cut from $c$ to $infty e^itheta_0$.




    Does both statements unambiguously define the branch cut of the function? If yes, which statement is more common/generally accepted?




    complex-analysis soft-question




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Just a small question on the notation of showing how the branch cut is chosen:




      $log(z-c)$ is defined as $arg(z-c)in[theta_0,theta_0+2pi)$ with straight branch cut.




      VS




      $log(z-c)$ is defined as having a branch cut from $c$ to $infty e^itheta_0$.




      Does both statements unambiguously define the branch cut of the function? If yes, which statement is more common/generally accepted?




      complex-analysis soft-question




      share|cite|improve this question











      Just a small question on the notation of showing how the branch cut is chosen:




      $log(z-c)$ is defined as $arg(z-c)in[theta_0,theta_0+2pi)$ with straight branch cut.




      VS




      $log(z-c)$ is defined as having a branch cut from $c$ to $infty e^itheta_0$.




      Does both statements unambiguously define the branch cut of the function? If yes, which statement is more common/generally accepted?





      complex-analysis soft-question





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









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      Szeto

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