Questions tagged [generalized-function]

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1answer
87 views

Integral giving a Dirac delta

I have the following type of integral Integrate[ r BesselJ[n, a r] BesselJ[n, b r], {r, 0, Infinity} (where a and ...
4
votes
0answers
120 views

Integration involving DiracDelta

I tried the following integration Integrate[DiracDelta[Tan[x]], {x, -4, 4}] I got 1 as the result. However, between -4 and 4 ...
7
votes
2answers
458 views

Legendre expansion of the Dirac delta function

There is a known expansion for the Dirac delta function in the interval $ (-1, 1) $ in terms of the Legendre polynomials as $$ \delta(x) = \sum_{k = 0}^{\infty} (-1)^k \frac{(4k + 1) (2k)!}{2^{2k + 1} ...
5
votes
3answers
333 views

DSolve fails to handle summation involving DiracDelta

Executing s = DSolve[{y''[x] + y[x]==Sum[DiracDelta[x-2^n]/2^n,{n,0,Infinity}],y[-Pi/2]==-1,y'[-Pi/2]== 0}, y[x], x] , I obtained ...
2
votes
1answer
86 views

Correcting HeavisideTheta in MM11.3 for generating the same results with UnitStep in MM5.2

The UnitStep was replaced with the HeavisideTheta after the version 6.0 (reference here), but some differences confused me ...
2
votes
1answer
118 views

Solving 2D convection-conduction equation via using Fourier integral transform: the disappearance of the convection term?(with code)

I am currently solving a 2D convection-conduction equation. The convection is only working on the x direction. The governing equation and its associated conditions are given as where T is the ...
11
votes
1answer
431 views

x DiracDelta[x] simplifies to 0, desired or a bug?

Bug introduced in 5.0 or earlier, persisting through 12.0. I encountered this when trying to answer this question: x DiracDelta[x] // Simplify (* 0 *) Is this a ...
12
votes
1answer
1k views

Laplacian and DiracDelta

It is known that: $\nabla^2 \dfrac{1}{|r-r'|} = - 4 \pi \delta^3(\vec{r}-\vec{r}')$. If I do that with Mathematica, I find: ...