- #1
Swati Jain
- 3
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Homework Statement
Find and classify the singular point for
f(z) = 1/ ( sin z - sin a)
Where a is an arbitrary real constant.
Homework Equations
f(z) = 1/ ( sin z - sin a)
Where a is an arbitrary real constant.
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 ??