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age 29
visits member for 2 years, 2 months
seen Nov 21 at 12:35

As time goes on, I grow more disillusioned with quantum field theory.


Oct
19
comment Reference for closed form integral of $\int_0^1 dz\,z^n/(z-a)$
Oh I feel stupid, as always. Anyway, should the sum actually read $\frac{z^n-a^n}{z-a}=\sum_{k=0}^{n-1} a^{n-k-1} z^k$? I'll have to check...
Oct
19
revised Reference for closed form integral of $\int_0^1 dz\,z^n/(z-a)$
added 2 characters in body
Oct
19
comment Reference for closed form integral of $\int_0^1 dz\,z^n/(z-a)$
That's a good question, and something that I should have mentioned. The answer appears to be a sum of polynomial in $1/a$ and logarithm. So I guess I am looking for something of the form: $\sum_n c_n(1/a)^n + \text{logs}$. where the $c_n$'s are explicitly given (in terms of factorials, or Harmonic numbers, etc..)
Oct
19
asked Reference for closed form integral of $\int_0^1 dz\,z^n/(z-a)$
Sep
24
awarded  Autobiographer
Jul
25
comment How do I turn my verbal argument into something formal in [Real Analysis]? (proving every compact set is bounded)
Naive Question from a layperson: but if every open cover has a finite subcover, doesn't that mean that there is an excess of open sets that is not really essential in providing the open cover?? Doesn't this mean I could shed a few open sets without compromising the original property of being an open cover?
Jul
25
comment Integrating $\int_0^1 dx\,\ln(x-a)/(x-b)$ paying attention to cuts.
Also, I can't understand why after item 3., the counter reset to 1. Please fix.
Jul
25
asked Integrating $\int_0^1 dx\,\ln(x-a)/(x-b)$ paying attention to cuts.
Jul
7
revised How do I obtain the taylor expansion of the matrix logarithm sum
added 32 characters in body
Jul
7
revised How do I obtain the taylor expansion of the matrix logarithm sum
added 34 characters in body
Jul
7
asked How do I obtain the taylor expansion of the matrix logarithm sum
Jul
2
awarded  Curious
Jun
20
comment What is the notation for taking negative imaginary values for roots of negative numbers?
But if I put a $\sqrt{x}^*$ in my formula, it will look non-analytic.
Jun
20
asked What is the notation for taking negative imaginary values for roots of negative numbers?
Jun
13
asked Klein Gordan equation with harmonic source function
Apr
27
awarded  Tumbleweed
Apr
20
asked Inhomogenous partial differential equation
Apr
1
revised WKB and asymptotic behavior of second order differential equation
added boundary condition to description of plot
Apr
1
comment WKB and asymptotic behavior of second order differential equation
The original Riccati equation is $y'(x) = -\frac{a}{x^{n+2}} y^2(x) + a b^2 \frac{e^{-2x}}{x^{n-1}}$. And there is no harm in choosing $y(1) = 1$ as the initial condition (that was the condition I used to generate the plot).
Mar
31
revised WKB and asymptotic behavior of second order differential equation
Fixed typos in problem section