# 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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### 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 ...
• 71
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### 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: ...
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1 vote
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### 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 ...
• 7,843
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### 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 ...
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1 vote
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### 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!...
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### 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 $\omega$ (...
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1 vote
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### 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(...
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### Handling singularities like (x-y) in the denominator while evaluating double integrals

I have to solve an Integral of the following type ...
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### 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 ...
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### 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? ...
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1 vote
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### 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 $k\approx 1000$? <...
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1 vote
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### Incorrect result of InverseFourierTransform

When executing in 13.2 on Windows 10, the command FourierTransform[DiracDelta@Cos[x], x, s] results in ...
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1 vote
45 views

I did this: ...
• 605
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### 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 : ...
• 605
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### 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]]) ...
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### 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 ...
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### 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] ...
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### The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
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1 vote
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### Wrong InverseLaplaceTransform? [closed]

Is this a bug? https://www.wolframalpha.com/input?i=InverseLaplaceTransform%5B1%2FSqrt%5Bt%5D%2C+t%2C+x%5D ...
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1 vote
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### 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: ...
1 vote
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### 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 ...
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1 vote
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### 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 ...
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### 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]. ...
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1 vote
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### What integrals can FourierTransform evaluate that Integrate` cannot?

FourierTransform can make sense of integrals that diverge according to Integrate. ...
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### 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 ...
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