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Jan
14
awarded  Nice Question
Dec
4
comment What are the 4th degree roots of $1$?
First, please use informative titles which relate to the question bodies. Second, this belongs on math.stackexchange as it is unrelated to physics. Third, googling "fourth root of one" gives many satisfactory answers, for example this one.
Aug
25
awarded  Popular Question
Aug
10
comment (Numerical) Integration in log space
@Ian, $Y_I$ is monotonically decreasing, and does vary over many orders of magnitude. I do not know the derivatives, $f'(x)$, but of course I could approximate them...
Aug
10
asked (Numerical) Integration in log space
Mar
21
awarded  Notable Question
Feb
12
accepted What is the etymology of 'sinc function'?
Feb
8
comment Numerical integration with divergent bounds
@Ian, you were right! Chebyshev-Gauss quadrature does seem to work fine. For posterity, scipy's integrate.quad
Feb
7
comment Numerical integration with divergent bounds
Thanks, g(x) is definitely non-negative throughout the domain of interest. I'll try to play around with the guassian quadrature some more!
Feb
7
comment Numerical integration with divergent bounds
@Ian, there's no analytic version of the function [$g(x)$ is based on data]. But for physical reasons, the integral between these bounds must be well defined.
Feb
7
awarded  Commentator
Feb
7
comment Numerical integration with divergent bounds
Thanks @Ian, that's a very helpful hint. I'm not sure the order of divergence. Is there a numerical way to find out?The scipy package's built-in Gaussian quadrature method fails for my function, so I assume Chebyshev polynomials (which I think it uses?) in particular don't work.
Feb
7
revised Numerical integration with divergent bounds
added 417 characters in body
Feb
7
comment Numerical integration with divergent bounds
Thanks! But I don't have an analytic expression for my function, it is purely numeric. I will amend my question to explain better.
Feb
7
comment Numerical integration with divergent bounds
@imranfat thats basically what I've already said. But, for the simplest numerical methods, you must evaluate your function at (or near) your endpoints to evaluate the integral.
Feb
7
revised Numerical integration with divergent bounds
added 571 characters in body
Feb
7
comment Numerical integration with divergent bounds
Thanks, that's what I tried first --- but as I make the poorly-behaved regions smaller, the difference between left and right reimann sums diverges... so I still wasn't getting a good approximation
Feb
7
asked Numerical integration with divergent bounds
Jan
16
awarded  Notable Question
Jan
6
awarded  Yearling