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2d
accepted How do I write a terminating series representation of $_2 F_1(p, n+1, n+2, x)$
Jul
23
asked How do I write a terminating series representation of $_2 F_1(p, n+1, n+2, x)$
Mar
15
asked How to study the asymptotic behavior of $f(r)=\int_0^1 dx\, \text{Li}_2\Big(1-\frac{r}{x(1-x)}\Big)$ for small $r$?
Dec
9
comment I am going mixed
the folks at math.stackexchange will tell you $(-1)^{2/2}\neq((-1)^2)^{1/2}$
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?
Apr
27
awarded  Tumbleweed
Apr
1
revised WKB and asymptotic behavior of second order differential equation
added boundary condition to description of plot