User Michael Engelhardt

43 votes

Why is the Fourier transform so ubiquitous?

answered Feb 11, 2020 at 20:58

40 votes

Accepted

Do we lose any solutions when applying separation of variables to partial differential equations?

answered Dec 26, 2020 at 5:37

23 votes

Is there a general solution for the differential equation $f''(x) = f(f(x))$?

answered Feb 17, 2021 at 5:23

20 votes

Why is resonance such a widespread phenomenon?

answered Sep 12 at 6:18

17 votes

Motivation and physical interpretation of the Laplace transform

answered Feb 15 at 5:19

15 votes

Accepted

How to compute $\sin(\frac{d}{dx})f(x)$?

answered Dec 18, 2022 at 14:12

15 votes

The Planck constant for mathematicians

answered Sep 11, 2019 at 17:39

12 votes

Papers on arXiv solving the same problem at the same time

answered Aug 24, 2019 at 3:08

12 votes

Accepted

A toy model in 0-d QFT

answered Oct 12, 2019 at 17:42

12 votes

Accepted

Is there a real-analytic way to derive the asymptotics of $\int_{-\infty}^\infty e^{ikx} e^{-k^4}\,dk$ as $|x|\to\infty$?

answered Nov 6, 2021 at 6:53

12 votes

How would you work out this integral as a series?

answered May 25, 2022 at 3:50

10 votes

Any real contribution of functional analysis to quantum theory as a branch of physics?

answered Dec 11, 2019 at 17:22

10 votes

Accepted

Taylor expansion of exponential of a Lie derivative

answered Jan 20, 2020 at 18:19

9 votes

Accepted

Limiting behavior of lattice sums

answered Sep 9, 2021 at 3:01

9 votes

Accepted

Taylor expansion of Stieltjes Transform

answered Jul 10, 2023 at 2:57

8 votes

Integral of the $\delta$ function

answered Jul 26, 2023 at 16:29

8 votes

When and where did Gauss say this

answered Jan 1, 2021 at 7:34

8 votes

Accepted

Periodic eigenfunctions for 2D Dirac operator

answered Dec 10, 2020 at 6:30

7 votes

Explicit eigenvalues of matrix?

answered Sep 9, 2021 at 3:54

6 votes

Accepted

Even and odd solutions for the Schrödinger equation

answered Jun 29, 2021 at 15:09

6 votes

Fourier cosine transform from Erdélyi's Tables of Integral Transforms

answered Aug 8, 2021 at 22:43

6 votes

Accepted

Diagonalise self-adjoint operator explicitly?

answered Jan 8, 2021 at 1:13

6 votes

Famous cases of multiple papers by the same author published in same issue of same journal

answered Oct 27, 2020 at 6:29

6 votes

Value of an integral

answered Sep 8, 2020 at 6:20

6 votes

1-dimensional pure gauge theory

answered Oct 12, 2019 at 18:41

6 votes

Is $A^2 + (A^2)^t$ Positive Semidefinite?

answered Aug 9, 2023 at 0:52

6 votes

Does there exist an electromagnetic analogue of Einstein's field equations?

answered Jun 12 at 6:46

6 votes

Accepted

Verify $ \limsup_{\epsilon \rightarrow 0^+} \int_{D}\frac{1}{\sqrt{(x-(1-\epsilon))^2 +y^2}}\frac{1}{\sqrt{1-\sqrt{x^2+y^2}}} \, dx \, dy <+\infty$

answered Aug 18 at 3:45

5 votes

Accepted

Generating function of the product of Legendre polynomials

answered Feb 11, 2022 at 7:46

5 votes

Accepted

Entire function not less than $\sqrt{\sinh x/x}$ on the real line

answered Oct 3, 2019 at 5:09

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111 Answers

Why is the Fourier transform so ubiquitous?

Do we lose any solutions when applying separation of variables to partial differential equations?

Is there a general solution for the differential equation $f''(x) = f(f(x))$?

Why is resonance such a widespread phenomenon?

Motivation and physical interpretation of the Laplace transform

How to compute $\sin(\frac{d}{dx})f(x)$?

The Planck constant for mathematicians

Papers on arXiv solving the same problem at the same time

A toy model in 0-d QFT

Is there a real-analytic way to derive the asymptotics of $\int_{-\infty}^\infty e^{ikx} e^{-k^4}\,dk$ as $|x|\to\infty$?

How would you work out this integral as a series?

Any real contribution of functional analysis to quantum theory as a branch of physics?

Taylor expansion of exponential of a Lie derivative

Limiting behavior of lattice sums

Taylor expansion of Stieltjes Transform

Integral of the $\delta$ function

When and where did Gauss say this

Periodic eigenfunctions for 2D Dirac operator

Explicit eigenvalues of matrix?

Even and odd solutions for the Schrödinger equation

Fourier cosine transform from Erdélyi's Tables of Integral Transforms

Diagonalise self-adjoint operator explicitly?

Famous cases of multiple papers by the same author published in same issue of same journal

Value of an integral

1-dimensional pure gauge theory

Is $A^2 + (A^2)^t$ Positive Semidefinite?

Does there exist an electromagnetic analogue of Einstein's field equations?

Verify $ \limsup_{\epsilon \rightarrow 0^+} \int_{D}\frac{1}{\sqrt{(x-(1-\epsilon))^2 +y^2}}\frac{1}{\sqrt{1-\sqrt{x^2+y^2}}} \, dx \, dy <+\infty$

Generating function of the product of Legendre polynomials

Entire function not less than $\sqrt{\sinh x/x}$ on the real line