A beautiful integral relating π and the golden ratio φpic.twitter.com/j7kAo2cFeG
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It is the Cauchy residue formula but the trick where you take the derivative of the denominator is only for simple poles. It’s actually quite useful for partial fractions
Yes, exactly.. my understanding is that these were for simple poles.. off the cuff I didn’t think these were simple poles or is my memory failing me?
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It is described here https://en.m.wikipedia.org/wiki/Residue_(complex_analysis)#Simple_poles … There can't be anything else here really, as the denominator only has isolated roots (of -1)
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huh, didn’t know about that special case of L’hopitals rule for the case of simple poles.. very useful!
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Roots of x^k+1 are all simple
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