Skip to main content

Questions tagged [generalized-function]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
0 answers
43 views

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 ...
Lichun Chang's user avatar
4 votes
3 answers
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 ...
Mohamed Mostafa's user avatar
1 vote
1 answer
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: ...
Max Kanwal's user avatar
2 votes
1 answer
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 ...
xiaohuamao's user avatar
  • 4,728
0 votes
0 answers
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 $x>0$ ...
math2021's user avatar
  • 749
0 votes
0 answers
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,...
Mathecis's user avatar
  • 153
0 votes
1 answer
165 views

Why is this integral divergent?

Integrate[DiracDelta[1 - y]*DiracDelta[y - 5], {y, 0, 10}] this is divergent integral but this ...
Fritz's user avatar
  • 1
2 votes
2 answers
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 ...
Marc Borrell's user avatar
4 votes
0 answers
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 ...
Dark Lord's user avatar
7 votes
2 answers
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} ...
user avatar
5 votes
3 answers
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 ...
user64494's user avatar
  • 27.1k
2 votes
1 answer
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 ...
likehust's user avatar
  • 693
2 votes
1 answer
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 ...
LingLong's user avatar
  • 329
11 votes
1 answer
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 ...
xzczd's user avatar
  • 67k
12 votes
1 answer
2k 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: ...
mattiav27's user avatar
  • 6,747