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Mathematics
General Math
Complex analysis - removable singular points
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[QUOTE="mathwonk, post: 6055732, member: 13785"] 1. there is no difference in integrating an analytic function versus a function with a removable singularity. more interesting is the case of a function which does not have a removable singularity but still has integral zero due to there being a pole there of higher order and residue zero. i.e. integral = 0 just means the term 1/z has coefficient zero, but therte could still be terms of order 1/z^2 or 1/z^3 etc with non zero coefficients but the integral will not detect that. 2. in this example sin has only odd degree terms of positive degree, and the linear term equals z, so subtracting off z reduces it to beginning in degree 3. thus dividing by z^3 gives an analytic function (i.e. one with a removable singularity). do not obsess over whether a function has or has not yet been stated as defined at a point when it is perfectly capable of being well defined there. all functions with removable singularities should have them removed, before studying the function. [/QUOTE]
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Complex analysis - removable singular points
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