# Questions tagged [generalized-function]

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### 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 ...
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 ...
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} ...
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 ...
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 ...
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 ...
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: ...