What is the Laurent Series for cosec(z)
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This video shows how to
This video shows how to find the Laurent Series of the function f(z) = csc(z) where z=a+bi and i=sqrt(-1) for the the function .
As x approaches zero from the +ve side cosec(x) approaches infinity.
As x approaches zero from the -ve side cosec(x) approaches negative infinity.
Therefore the limit for cosec(x) as x approaches zero does not exist
The first part is to see that the Taylor Series for csc(x) is undefined hence this is a Laurent Series.
Then we used the Taylor Polynomial for sin(z) up to z^ 7and took the reciprocal. This creates a large polynomial long division question.
A big part of what we need next is to find the reciprocal of the sine function. Much of this is done via Polynomial Long Division.
The last part is to do the Long Multiplication.
Here is that video
• Find Residues of a cosec Function wit...
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