>>11285263>dude i believe you, i truly do, but i have no fucking idea what r u talking about, its not my uni so i stuck a lot on that, im not realy understand theory that well, im sorryin complex analysis, if you have a function f(z) that converges to some w as |z|->infinity, then lim(g(z)), where g(z) = f(1/z) for z =/= 0, as z->0 is w. if you define g(0) = w, then g is continuous at 0. if this function happens to be holomorphic at the origin, then it has a laurent series expansion valid in some neighborhood around the origin. taking the reciprocal of z in that series will give you a series representation of f that is valid outside some neighborhood of 0.
afaik atan(z) is discontinuous along its branch cut, and so it is not holomorphic at infinity. atan(1/x) has a jump discontinuity at 0. i don't exactly know how wolfram alpha gets the series expansion at infinity.
i'm guessing it has to do with the fact that its derivatives do not have a jump discontinuity at 0, and so as in
>>11285343you can just take the limit of atan as x goes to positive infinity, and then evaluate the derivatives of atan(1/x) at 0 as normal.
i'd like to read the relevant theorems if anyone knows them.
