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Mar
8
comment Understanding the integral of $x^a$
In Taylor series and Laurent series we think of $x^0 = 1$. I wonder if there is an alternative series expansion which uses the logarithm for the 0th power. If I remember correctly there is a problem with the logarithm in conventional complex analysis, because the singularity at 0 is a strange kind of singularity. Or maybe I'm talking nonsense...
Mar
8
accepted Understanding the integral of $x^a$
Mar
8
comment Understanding the integral of $x^a$
I'll ask a follow-up question if you don't mind. I hope it is not too vague. Does this mean that in some sense the logarithm ought to belong to some extension of the set of polynomials with integer exponents, where the logarithm is related to $x^0$?
Mar
8
comment Understanding the integral of $x^a$
Thanks, that does help, but it does not completely resolve my confusion. I feel like there is something going on with the order of the limits, because if you have the limit of $3^a/a$ as $a$ goes to 0 then it's not $\log 3$. What am I missing? edit: oh, I already see my mistake, thanks! I was confused because I only looked at the indefinite integral.
Mar
8
asked Understanding the integral of $x^a$
Nov
9
awarded  Editor
Nov
9
revised Why is Newton's method faster than gradient descent?
edited title
Nov
9
asked Why is Newton's method faster than gradient descent?
May
7
awarded  Scholar
May
7
comment Numerical optimization with nonlinear equality constraints
Thanks, that's exactly what I was looking for!
May
7
accepted Numerical optimization with nonlinear equality constraints
Apr
10
awarded  Student
Apr
10
asked Making sense of the big world of gradient methods
Sep
22
asked Numerical optimization with nonlinear equality constraints
Oct
25
comment Which one is bigger $2^{n!}$ or $(2^{n})!$?
What can we say about f(g(n)) relative to g(f(n)) in general?
Feb
22
awarded  Supporter
Feb
22
comment Where is the flaw in this argument of a proof that 1=2? (Derivative of repeated addition)
A simpler version: 1+1+...+1 repeated x times = x. Now you can see that the left hand side is obviously not constant with respect to x.