I want to take the inverse Fourier transform of the following function:

$$ \hat{f}(\omega) = \begin{cases}e^{-r  \sqrt{\omega}} &amp; \text{for } \omega &gt; 0 \\ 0 &amp; \text{otherwise}\end{cases},$$ 

such that

$$ f(t) = \int_{-\infty}^\infty \hat{f}(w)e^{i\omega t} d\omega= \int_0^\infty e^{-r \sqrt{\omega}} e^{i\omega t} d\omega,$$ 

where $r$ is a constant.

I am having trouble in integrating this. That $ \sqrt{\omega}$ is ruining my day. Any suggestions?

Kind regards


Question: how to install .net framework? if not already installed using autorun.inf
Answer: Here is a not tested batch code which makes more sense then your batch code:

@echo off
setlocal
set "RetryCount=0"
:ReCheckFramework
%SystemRoot%\System32\reg.exe query "HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\NET Framework Setup\NDP\v4\Full" /v Version&gt;nul 2&gt;nul 
if not errorlevel 1 goto EndFrameworkInstall
start "Install FrameWork" /wait dotNetFx40_Full_x86_x64.exe
set /A RetryCount+=1
if %RetryCount% LSS 3 goto ReCheckFramework
:EndFrameworkInstall
endlocal


Testing a batch file should be always done by opening a command prompt window and running the batch file from within this console window. Then syntax errors and errors on parameter list of commands and applications can be easily seen.

reg.exe requires as first parameter the action to do, here query. And you forget the double quotes around registry key as it contains spaces.

Also writing nearly all commands in one line is also wrong.

Well, best would be to really check version of installed .NET Framework 4 in case of a newer version is already installed then what is put on CD/DVD.