1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find and classify singularity?

Tags:
  1. Oct 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Find and classify the singular point for
    f(z) = 1/ ( sin z - sin a)
    Where a is an arbitrary real constant.

    2. Relevant equations
    f(z) = 1/ ( sin z - sin a)
    Where a is an arbitrary real constant.

    3. The attempt at a solution
    There will be infinite number of singularities of sin z = sin a
    Put z' = z-a
    Denominator can be written as sin z - sin a = sin ( z'+ a) - sin a
    = sin a cos z' + cos a sin z' - sin a = sin a ( cos z' - 1) + cos a sin z'
    = sin a ( -1/2! Z'^ 2 + 1/4! Z'^ 4 + ......) + cos a ( z' - z'^ 3/3! +......)
    = cos a z' - 1/2! Sin a z'^2 -.........
    Now how to define a and singularities ??
     
  2. jcsd
  3. Oct 28, 2015 #2

    RUber

    User Avatar
    Homework Helper

    What if you look at the solution set to the problem:
    ##\sin a = \sin z##.
     
  4. Oct 28, 2015 #3
    I thought in this way too.. But I could not find how to find relation between z and a. It may be z = a + 2n pi, But I am not sure. And further I don"t understand that how to find singularity in this case. Thanks for your response.
     
  5. Oct 28, 2015 #4

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    Maybe you can use the formula for a difference of sines:

    ##\sin z - \sin a = 2\sin(\frac{z-a} {2})\cos(\frac{z+a} {2})##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find and classify singularity?
  1. Singularity functions (Replies: 1)

  2. Singularities in GR (Replies: 3)

Loading...