# Questions tagged [generalized-function]

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### Issue about simplify dirac delta function [duplicate]

When I trying to simplify a dirac delta equation, I got the following result. The result confused me. How can I make the second equation output true ...
225 views

### Integration involving two DiracDelta with variable limit

I want to write a code to evaluate $$\int_0^{t-1}\frac{\delta(z-1)}{z}\frac{\delta(t-z-1)}{t-z}dz$$ which should gives the answer $$\frac{\delta(t-2)}{t-1}.$$ I tried to write the code ...
1 vote
84 views

### Dynamically generate system to use with NDSolve

I have a d-dimensional differential equation that I want to solve that takes the following form: When d = 1: ...
293 views

### How to calculate infinitesimal analytic continuation?

Many problems in science and engineering are related to the analytic continuation and in particular infinitesimal analytic continuation to the upper or lower complex plane, i.e., a generic complex ...
• 4,728
48 views

### How to find the sequence function $f(n,x)$ of the three given functions?

I have the three functions $f(2,x)$, $f(3,x)$ and $f(4,x)$ where $x>0$ ...
• 749
86 views

### Non linear first DE with lot of parts

I want to know how I can solve this equation in Mathematica I guess I missed something!! DSolve[ {a (h[a])^2 h'[a] +(nh[a]/ a^2) + m(h[a])^3 - l (h[a])^2 - t == 0}, h, a] h[a] is my function and n,m,l,...
• 153
165 views

### Why is this integral divergent?

Integrate[DiracDelta[1 - y]*DiracDelta[y - 5], {y, 0, 10}] this is divergent integral but this ...
934 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 ...
136 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 ...
3k 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} ...
441 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 ...
• 27.1k
114 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 ...
• 693
283 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 ...
• 329
507 views

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

Bug introduced in 5.0 or earlier, persisting through 13.0. I encountered this when trying to answer this question: x DiracDelta[x] // Simplify (* 0 *) Is this a ...
• 67k
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: ...