# 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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### 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, ...
123 views

### Strange result simplifying higher order BesselJ

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
72 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: ...
94 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
117 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 ...
1 vote
87 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. ...
86 views

312 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] ...
80 views

### LaplaceTransform doesn't work

I have code: A = 1; ω0 = 5*10^6; τ0 = 3*10^-3*Sqrt[2/Log]/(5.85*10^3); s0[t_] = A*E^(-t^2/τ0^2)*Cos[ω0*t]; Phi[ω_] = LaplaceTransform[s0[t], t, ω] The last ...
59 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] ...
203 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 ...
44 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? ...
1 vote
153 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 ...
170 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}...
123 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
34 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 ...
114 views

384 views

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

FourierTransform can make sense of integrals that diverge according to Integrate. ...
145 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 ...
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. ...
1 vote
159 views

### Convert complex exponential to real exponentials, sines and cosines

While taking the inverse Laplace transform of certain expressions, Mathematica yields complex exponentials. For example, using the following code: ...
161 views

### LaplaceTransform works well with x[t], but doesn't recognize x[t], how to make it works for x[t]?

Bug introduced in 12.2(?), persisting through 13.2 or later. When I am solving odes using LaplaceTransform, I found that LaplaceTransform works well with u[t] or y[...
149 views

### How to guide Eliminate or GroebnerBasis to reduce a set of simple odes to a single ode (which can be done by Laplace Transform)

Recently, I am trying to use Eliminate or GroebnerBasis to simplify a system of ODEs. I don't want the solution of ODEs. What I ...