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seen Jun 11 at 10:57

May
28
comment General expression for hypergeometric function ${}_1F{}_1(p, 1, x)$ when p is an integer
it seems the answer is Sum[(-x)^k/k!/(k + 1) Binomial[p, k], {k, 0, p}]==Hypergeometric1F1[-p, 2, x]
May
27
comment General expression for hypergeometric function ${}_1F{}_1(p, 1, x)$ when p is an integer
Ok never mind! What motivated the conjecture?
May
27
comment General expression for hypergeometric function ${}_1F{}_1(p, 1, x)$ when p is an integer
Would you know what Hypergeometric1F1[p, 2, x] could be? Its the only other one I need :-)
May
27
comment General expression for hypergeometric function ${}_1F{}_1(p, 1, x)$ when p is an integer
More generally its If[p > 0, Exp[x] LaguerreL[p - 1, -x], LaguerreL[-p, x]] for negative p to work as well.
May
27
comment General expression for hypergeometric function ${}_1F{}_1(p, 1, x)$ when p is an integer
Thanks so much! Its related to the spin of galaxies in large scales structures as it happens
May
26
comment What is the generalization of Gauss's Theorem to a manifold?
I friend of mine (whom I passed your question) tells me that the answer to your question is on p. 147 & 148 of “Geometrical methods of mathematical physics” by Bernard Schutz. Regards
Apr
6
comment Perturbation theory PDEs
I would argue this was not your original post.
Mar
27
comment Perturbation theory PDEs
If you apply the above procedure iteratively n times it will provide you with a solution up to order ϵ^n. What would be a converged solution in your view? Compared to a numerical solution?
Mar
27
comment Perturbation theory PDEs
It obeys the original equation at order ϵ^2 so that is more or less the definition of a perturbative solution. Note that the method would also work for the full blown problem of Ψ(r,t,p) it would just be more messy.
Mar
26
comment Perturbation theory PDEs
@Lipschitz could you please explain to me why my answer is not answering your question?
Mar
23
comment Perturbation theory PDEs
@Lipschitz it is rigorous! At least for a physicist :-)
Mar
23
comment Perturbation theory PDEs
But your question claims actual solution is known, so I it is fair to assume the square is known too?
Mar
23
comment Perturbation theory PDEs
Naively (as a physicist), one would write $\Psi=\Psi_0+\epsilon \Psi_1$. Replace in original equation assuming $\Psi_0$ solves original equation. Get a new (linear) equation for $\Psi_1$ involving r.h.s. with (known) $\Psi_0^2$… iterate?
Sep
17
comment Evaluate $\int_1^\infty \cosh^{-1}(x) \ln(x^2-1) \exp \left(- \frac{x}{T} \right) dx $
Thanks! Very impressive! FYI this computation was needed for this paper fr.arxiv.org/pdf/1211.7352 for which we gave up presenting the corresponding anisotropic closed form.
Dec
15
comment Change of variables in Belousov-Zhabotinsky reaction
Could you please change you title to something more specific? Thanks
Nov
27
comment Definite integral over triple products of higher order Bessel functions.
@Phira thanks for the advice; it seems difficult to do in practice since 3 such functions are involved??
Nov
27
comment Integral over triple product of spherical Bessel functions
Thanks a lot! It always looks so simple in retrospect; I feel a bit embarrassed.
Jun
29
comment Evaluate $\int_1^\infty \cosh^{-1}(x) \ln(x^2-1) \exp \left(- \frac{x}{T} \right) dx $
It arises in the context of Faraday polarization transfer.
Jun
4
comment Does the integral of PDF of multi-normal distribution over quarter planes have a closed form?
Nor does its cumulative distribution reduces to any analytic form?
Jun
4
comment Does the integral of PDF of multi-normal distribution over quarter planes have a closed form?
Is it correct to assume there is no generalization of the Owen's T function which would be applicable to the 3D case?