# 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.

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### Same integral giving different results

I am trying to solve the following integral using Mathematica $\int_{0}^1 dz \int_{0}^{1} dz' \exp(-k|z-z'|)\cos[\pi p z] \cos[\pi q z]$, with $p,q\in \mathbb{Z}$. To do so, I am doing the following: <...
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### Does anyone know what the 2D Hilbert transform is of exp(-(x+y)^2)? [migrated]

I'm having no luck finding the 2D Hilbert Transform (standard principle value definition) f(x,y)=exp(-(x+y)^2). Naively I might expect this to be zero since under change of variables (rotation) to u=(...
62 views

### Cannot Solve the Following Equation in Laplace Domain Using DSolve

I’m trying to solve the following ODE with two boundary conditions in the Laplace domain, but I’m encountering an error. Any advice would be greatly appreciated. Here is the code ...
121 views

### LaplaceTransform and DSolve handles PDE well in version 14, but not in 13.3

I'm facing an error when trying to solve a simple Laplace-transformed PDE with one basic boundary condition, followed by applying the InverseLaplaceTransform. The ...
189 views

### Laplace transform on boundary condition of PDE results in D::ivar warning

Bug introduced in 14.0, persisting through 14.1. I am trying to convert my boundary condition to its Laplace transform as in this picture: I have tried to do so using the following code: ...
177 views

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### 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 ...
205 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 ...
86 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 ...
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1 vote
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### 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, ...
• 453
142 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....
1 vote
83 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: ...
101 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 ...
1 vote
130 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 ...
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1 vote
112 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. ...
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113 views

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] ...
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96 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 ...
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] ...
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230 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 ...
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### 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? ...
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1 vote
197 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 ...
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### 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}...
148 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 ...
1 vote
37 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 ...
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• 187
1 vote