# Questions tagged [differential-calculus]

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### How to relate this integration with the integral expansion of special functions?

I encounter the following integral when trying to find the inverse Fourier transform of the characteristic function of a certain sum of random variables. Here, $p\ge0$, $q\ge0$ are real, and $n,a,b$ ...
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### Does the homeomorphism have a non-negative or non-positive determinant?

Let $\Omega_1$ and $\Omega_2$ be domains (open and connected) in $\mathbb{R}^2$. $\psi:\Omega_1\to\mathbb{R}$ and $\phi:\Omega_1\to\mathbb{R}$ are $C^1$ functions with two variables. ...
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### Second order partial derivatives of Sobolev functions

This has been asked on Mathematics Stack Exchange but apparently received no attention. The question is very basic in nature: Is it true that $W^{2,1}_{\text{loc}}$ functions (after possibly modifying ...
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### An expression for the $k$-th derivative of $f(x)=x^n\exp(-x)$ [closed]

Is there a finite expression for $k$-th derivative of \begin{align} f(x)={x^n}{e^{ - x}} \end{align}
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### Solving $\frac{dy}{dx}=1+(a_mx^m+a_{m-1}x^{m-1}+...+a_0)y^2$

I have a problem with the following equation, $\frac{dy}{dx}=1+P_m(x)y^2$ Where $P_m(x)$ is a polynomial function. I have solution for $P_m(x)=x$ using Mathematica, and Prof @Claude Leibovici solved ...