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programming numerical algorithms for astrophysical applications.


Sep
30
awarded  Scholar
Sep
30
accepted General solution to first-order ODE in 3D
Sep
29
comment General solution to first-order ODE in 3D
thanks. So I learned about the matrix exponential. Great! (I would accept this comment morphed into an answer ...)
Sep
28
asked General solution to first-order ODE in 3D
Sep
24
awarded  Autobiographer
Sep
3
comment Analyze rotation of satellite orbit due to transverse acceleration.
I've answered this question here.
Jun
29
comment integral of spherical harmonics over cube
I wanted to know the multipole moments of constant density cube. So knowing which vanish is only part of the story. I also need the value for those which don't. Preferrably not the numerical value, but a closed formula.
Feb
4
comment Wanted: simple invertible function with specified derivative properties
@copper.hat Sorry, that fails: $F''(0)\neq0$.
Feb
3
revised Wanted: simple invertible function with specified derivative properties
deleted 9 characters in body
Feb
3
revised Wanted: simple invertible function with specified derivative properties
added 2 characters in body
Feb
3
revised Wanted: simple invertible function with specified derivative properties
added 2 characters in body
Feb
3
asked Wanted: simple invertible function with specified derivative properties
Dec
28
awarded  Commentator
Dec
28
comment integral of spherical harmonics over cube
This is not what I was looking for. I had worked out a similarly tedious way myself (before asking), but was looking for a more compact formula. Thanks for your efforts anyway.
Dec
28
comment expectation value for minimum distance between random variables
@Eckhard I'm only interested in the limit of large $n$ (I should have said that, sorry).
Dec
27
comment integral of spherical harmonics over cube
@user86418 Yes, this is all obvious, but doesn't provide me with a closed expression (or at least a recursion) for the $I_n^m$.
Dec
26
comment integral of spherical harmonics over cube
Yes, I know all of them. What I want is recursion (or otherwise) for the $I_n^m$ ... And of course, $U^m_n=\sum_{i,j,k}a^{nm}_{ijk}x^iy^jz^k$, i.e. the coefficients carry 5 indices, not 3.
Dec
25
comment integral of spherical harmonics over cube
@user86418 (i) or (iii) would be okay. And yes, using the Cartesian form of the harmonics is perfectly okay.
Dec
22
comment nonlinear transform of Gaussian random variable that preserves Gaussianity
@RobertIsrael I missed that your $\boldsymbol{Y}$ was a random variable.
Dec
21
comment expectation value for minimum distance between random variables
@PeterKoŇ°inár You're absolutely correct. There was a bug in my simulation. I fixed it. It's $1/n^2$.