Skip to main content

Questions tagged [integral-transforms]

Questions about transforms of functions by means of integration, such as Fourier transforms and Laplace transforms. Many integral transforms can be inverted by means of another integral transform.

Filter by
Sorted by
Tagged with
1 vote
2 answers
113 views

Different solutions between Mathematica and Wolfram Alpha

I started to use Mathematica just recently and tried to do the following simple integral: The result I get from Integrate[1/(Exp[x]+1),x] is ...
Tommy's user avatar
  • 71
3 votes
2 answers
114 views

InverseLaplaceTransform returns the input

Initially, I was trying to invert the following expression: $$ \frac{e^{-a\sqrt s}}{s-c} $$ and got the following result: ...
KNVCSG's user avatar
  • 31
1 vote
1 answer
117 views

Partial integro-differential equation

I want to solve the following partial integro-differential equation for $\delta(x,t)$: $$ 1-B \cdot \frac{\partial \delta(x, t)}{\partial t}=\frac{1}{\pi} \int_{-1}^1 \frac{\partial \delta(s, t)}{\...
Rui's user avatar
  • 11
0 votes
1 answer
75 views

On the Laplace transform of Beta function

While trying to evaluate the Laplace transform below $$I = \int_{0}^{\infty}e^{-st}B(\frac{1}{2}-it,\frac{3}{2}+it)\mathrm{d}t,$$ invoking ...
User's user avatar
  • 103
3 votes
3 answers
191 views

Wolfram Alpha and Wolfram Engine produce different Laplace transforms

Consider the following Laplace transform: $$\mathcal{L}\{\dfrac{\sin{2x}}{x}\}$$ To calculate it, I'd write LaplaceTransform[Sin[2 x] / x, x, p] into both Wolfram ...
Mehrshad Khansarian's user avatar
3 votes
1 answer
79 views

Solving Laplace Transform IVP [closed]

I want to solve the IVP Laplace transform for the following: $$y''-2y'+y=3e^t$$ with $$y(0)=1, \; y'(0)=1.$$ How would I input this in Wolfram Language? I've tried a bunch of different things and ...
JasonF's user avatar
  • 33
1 vote
1 answer
73 views

Is there an option for InverseLaplaceTransform to make Mathematica use the convolution theorem when feasible?

By default, it appears that Mathematica won't use the convolution theorem to write an inverse Laplace transform in the form of a convolution of two functions. For example, ...
Matt's user avatar
  • 453
4 votes
1 answer
139 views

Strange result simplifying higher order BesselJ [duplicate]

Consider the following integral: $$\int_0^1 Z_n^m(r)\ J_m(\rho r) r dr$$. The solution of this should contain a single Bessel function: $$(-1)^{(m-n)/2}\ J_{n+1} (\rho)/\rho$$ (see https://www.osti....
AstronomyGeek's user avatar
1 vote
0 answers
81 views

How can I write the code for an inverse integral transform?

How can I code any type of integral transform with its inverse integral transform in Mathematica which gives the correct results and properties? Below is the example for Elzaki transform: ...
Kishor Kshirsagar's user avatar
5 votes
1 answer
100 views

InverseFourierSinTransform on Mathematica did not give a result

I am trying to solve the linear Schrödinger equation with the Fourier transform. I have difficulty making the corresponding graph when I solve the problem numerically. Can you explain to me what is my ...
Athanasios Paraskevopoulos's user avatar
1 vote
1 answer
129 views

How to deduce analytical solution from numerical solution

I came across one such integral in my calculations, for which there is no analytical solution. But it exists numerical solution, so how can I derive analytical solution of this integral from numerical ...
little star's user avatar
1 vote
1 answer
101 views

Question about numerical integration of a double integral

I am trying to numerically integrate the following double integral in Mathematica for different values of t. ...
HadamardN2's user avatar
0 votes
1 answer
111 views

Taking the inverse Laplace Transform as a vector operation

I am solving a system of first-order equations using matrix operations and the Laplace Transform. I begin with the matrix equation that represents the solution to my system, like this: $$ \underline{\...
villaa's user avatar
  • 187
8 votes
3 answers
535 views

Inverse Laplace Transform of Hypergeometric function

Any tips how to massage the following to get computed by Mathematica for $p>1$? I suspect the result should be expressible in terms of exponential integral ...
Yaroslav Bulatov's user avatar
5 votes
1 answer
109 views

NIntegrate with highly oscillatory Bessel and hypergeometric integrands

I am trying to compute the following double integral int2[n_] := NIntegrate[ n^2 * u * BesselJ[0, u]^n * r^2 * BesselJ[0, n*r*u], {r, 0, 1}, {u, 0, Infinity}] for ...
epsilone's user avatar
  • 153
1 vote
2 answers
63 views

InverseFourierSinTransform in mathematika failed to give a result

I have to use InverseFourierSinTransForm in Mathematika for the function u[ω,t] but infortunately it does not work.It gives back the same! I tried it without the assumptions but it does not work again!...
george's user avatar
  • 43
2 votes
1 answer
125 views

Derive Parseval's theorem in one dimension

Parseval's theorem (in one dimension) is a fundamental result in the theory of Fourier transforms. If $f(t) \Leftrightarrow F(\omega )$ are Fourier transform pairs and $t$ (time) and $\omega$ (...
David G. Stork's user avatar
1 vote
1 answer
113 views

Evaluating Fourier transform in mathematica [closed]

I am trying to evaluate the expression FourierTransform[[m (a^2 - t^2 - I g t)]^-1, t, ω] in Mathematica. It gives me the error message that "Syntax: "[m(...
Solidification's user avatar
0 votes
1 answer
73 views

Handling singularities like (x-y) in the denominator while evaluating double integrals

I have to solve an Integral of the following type ...
Sourav Das's user avatar
2 votes
0 answers
62 views

Efficient powers of DPR1 matrices

I'm looking to compute the following quantity for $A$ where $A$ is a convergent positive definite $d\times d$ diagonal + rank1 matrix (DPR1). $$f(s)=\operatorname{Tr}(A^s)$$ Earlier answer answer by ...
Yaroslav Bulatov's user avatar
0 votes
1 answer
53 views

Improving quality of plot with bad numeric performance

I have a plot which suffers from poor numeric accuracy, any tips on how I can improve the quality of this plot? ...
Yaroslav Bulatov's user avatar
1 vote
0 answers
61 views

Inverting Laplace transform numerically for a set of points

Computing inverse of Laplace transform numerically in Mathematica seems very slow and requires $k$ calls for $k$ points. Is there a faster way to do it for a set of $k$ points, ie $k\approx 1000$? <...
Yaroslav Bulatov's user avatar
1 vote
0 answers
74 views

Incorrect result of InverseFourierTransform

When executing in 13.2 on Windows 10, the command FourierTransform[DiracDelta@Cos[x], x, s] results in ...
user64494's user avatar
  • 27k
1 vote
0 answers
45 views

What is the basis of the Fourier transform in Mathematica? [duplicate]

I did this: ...
Superunknown's user avatar
0 votes
0 answers
54 views

Hilbert Transform in mathematica [duplicate]

I would like to do a Hilbert transformation in Mathematica on a function. However, it does not seem to give a right result. The Hilbert transform is given by So I did : ...
Superunknown's user avatar
5 votes
1 answer
216 views

Incorrect result of FourierTransform

Let us consider in 13.2 on Windows 10 FourierTransform[1/Sinh[x]^2, x, k] -((2 + k \[Pi] Coth[(k \[Pi])/2])/Sqrt[2 \[Pi]]) ...
user64494's user avatar
  • 27k
6 votes
1 answer
622 views

Wrong result of Laplace Transformation [closed]

I am trying to calculate the Laplace Transformation of the following function: $$f(x) = \theta(t+1)-\theta(t-1)$$ where $\theta(t)$ is the Heaviside step function defined as: $${\displaystyle \theta(x)...
Konstantinos Zafeiris's user avatar
8 votes
1 answer
325 views

Still bug in Integrate. 3

Let us consider in version 13.1 on Windows 10 r = Integrate[1/(x - a)/Sqrt[1 - x^2], {x, -1, 1}, Assumptions -> a \[Element] Reals] ...
user64494's user avatar
  • 27k
0 votes
0 answers
94 views

LaplaceTransform doesn't work

I have code: A = 1; ω0 = 5*10^6; τ0 = 3*10^-3*Sqrt[2/Log[2]]/(5.85*10^3); s0[t_] = A*E^(-t^2/τ0^2)*Cos[ω0*t]; Phi[ω_] = LaplaceTransform[s0[t], t, ω] The last ...
Cpp Nosavvier's user avatar
2 votes
0 answers
60 views

Is this a bug in InverseLaplaceTransform or LaplaceTransform?

Let us consider in version 13.1 on Windows 10 ClearAll["Global`*"]; a = InverseLaplaceTransform[s*Log[(s - 1)/(s + 1)], s, x] ...
user64494's user avatar
  • 27k
4 votes
1 answer
221 views

Inverse Laplace Algorithm used in Mathematica [closed]

I have a general question. I want to know what algorithm (The name of this numerical method) is already used to calculate a numerical Inverse Laplace in Mathematica. I used the function ...
Ali AlCapone's user avatar
2 votes
1 answer
45 views

Validation of the Laplace inversion and storage in a table or an array

I tried to validate this function from 0 to 50 but it takes very long time, is there a faster way to validate this function for t from 0 to 50 and add them in a list? ...
Ali AlCapone's user avatar
1 vote
0 answers
190 views

Inverse Laplace in mathematica

I can't even get an inverse Laplace for this expression numerically in mathematica, is there a way to inverse this equation below? I have also tried to use fixt talbot package for a numerical ...
Ali AlCapone's user avatar
0 votes
2 answers
172 views

Inverse Triple Laplace Transform of $\frac{-1}{s^2_{1} + s^2_{2} + s^2_{3}}$

I want to find the inverse triple Laplace transform of $L^{-1}_{x_{3}} L^{-1}_{x_{2}} L^{-1}_{x_{1}} \left[ \frac{-1}{s^2_{1} + s^2_{2} + s^2_{3}} \right]$. I did \begin{align*} L^{-1}_{x_{3}} L^{-1}...
Abdulhameed Qahtan Abbood Alta's user avatar
0 votes
1 answer
143 views

Fourier Transform of Integral Expression

I am trying to Fourier transform an expression containing an integral like this: FourierTransform[Integrate[f[v]*Cos[w[v]*t],{v,-v_0,v_0}],t,k] where ...
raeel's user avatar
  • 1
1 vote
0 answers
35 views

Replace subexpression with variable in result from Laplace transform

I'd like to clean up the result I obtained from an inverse Laplace transform: First of all, I'd like to replace the square root expressions in the hyperbolic function arguments (part encircled in ...
Hans's user avatar
  • 11
0 votes
0 answers
140 views

Implementing the 3D Radon transform

I am wondering how to implement the Radon transform, the 3D Radon transform, that is, given a 'density' function $f: \mathbb{R}^3\to \mathbb{R}$ The Radon transform of $f$ is $$Rf(s,w)= \int_{x\cdot w=...
NotaChoice's user avatar
3 votes
1 answer
149 views

FourierCosTransform bug?

Bug introduced in 13.0 or earlier and persisting through 13.2.0 or later. FourierCosTransform[Cos[(k + p) z], z, q] gives correct result ...
SantaP's user avatar
  • 845
2 votes
0 answers
81 views

InverseLaplaceTransform gives inconsistent results

These should give the same results, but they do not: InverseLaplaceTransform[1/Sqrt[x] HeavisideTheta[x + 1], x, y] InverseLaplaceTransform[1/Sqrt[x], x, y] ...
Anixx's user avatar
  • 3,606
0 votes
1 answer
89 views

The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
step-by-step's user avatar
1 vote
0 answers
89 views

Wrong InverseLaplaceTransform? [closed]

Is this a bug? https://www.wolframalpha.com/input?i=InverseLaplaceTransform%5B1%2FSqrt%5Bt%5D%2C+t%2C+x%5D ...
Anixx's user avatar
  • 3,606
1 vote
1 answer
82 views

Inverse Laplace transform of two coupled equations in Mathematica [closed]

I want to solve these coupled equations in Mathematica for F1(s) and F2(s) and the inverse Laplace of each of them to find c1(t) and c2(t). the code I tried is: ...
Mohadese Forouzesh's user avatar
1 vote
1 answer
96 views

Inverse Fourier Transform and the sign of the Shifted Delta

I am using the sign convention of FourierParameters->{0, -2 Pi} for calculating the inverse FT of $Aexp(-2\iota\pi f K)$, where $A$, $K$ are real numbers >0 ...
AChem's user avatar
  • 123
1 vote
0 answers
89 views

Implementing the Shift Property of the Fourier Transform in Mathematica

I am trying to determine the Fourier tranform of a time shifted (t-b) Lorentzian function in Mathematica. With the zero centered Lorentzian (b=0), the Integrate function with the conditions that all ...
AChem's user avatar
  • 123
2 votes
1 answer
122 views

How to calculate an `InverseMellinTransform` up to its definition in Mathematica?

I have a question about how to calculate Inverse Mellin Transformation's in Mathematica, one way or the other. Look at these findings. The following integral results in Gamma[s]. ...
nilo de roock's user avatar
1 vote
1 answer
419 views

How to do that Fourier transform?

I want to perform Fourier Transform of $$\frac{\exp(jkr)}{r},$$ where $k=\frac{2 \pi}{\lambda}$ and $r=\sqrt{x^2+y^2+z^2}$. The result should be $\exp\left(jkz \sqrt{1-(\lambda u)^2 - (\lambda v)^2} \...
Neysa's user avatar
  • 19
1 vote
1 answer
427 views

How to let Mathematica return impulse or Dirac delta functions when computing integrals?

For example, let's say I want to compute the (continuous-time) Fourier transform of the signal/function $\cos{(3t)}$, which is given by the following improper integral: $\displaystyle\int_{-\infty}^{\...
alejnavab's user avatar
  • 453
6 votes
1 answer
422 views

What integrals can `FourierTransform` evaluate that `Integrate` cannot?

FourierTransform can make sense of integrals that diverge according to Integrate. ...
John Doty's user avatar
  • 13.8k
3 votes
1 answer
159 views

Inverse Laplace Transform of function containing ArcTanh

I'm after the numerical inverse Laplace transform of a function, so I type f[t_?NumericQ] := InverseLaplaceTransform[1/(1 + s + ArcTanh[1/(s - 1)]), s, t]; This ...
sonarventu's user avatar
0 votes
0 answers
46 views

How to do variable change for a general Fourier series? I failed at first step :(

Well, firtly, I think I should define a general rule for Fourier series, but I fails. Below is my code including several attempts. Anys helps are greatly appreciated, thanks. ...
op-luffy's user avatar

1
2 3 4 5