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## how to delete unwanted space with a function or macro

 From: Uwe Brauer Subject: how to delete unwanted space with a function or macro Date: Sat, 08 Jan 2022 08:59:11 +0100 User-agent: Gnus/5.13 (Gnus v5.13) Emacs/29.0.50 (gnu/linux)

Hi

I just used plain align on the table below.

\begin{tabular}{|l|l|}
\hline
$$f(t)=\mathcal{L}^{-1}\{F(s)\}$$ & $$F(s)=\mathcal{L}\{f(t)\}$$ \\
\hline
1.                      & $$\frac{1}{s},\quad s>0$$             \\
\hline
2.$$e^{a t}$$                 & $$\frac{1}{s-a} \qquad s>a$$                      \\
\hline
3.                      $$t^{n}, \quad n=$$
positive                   integer                          &
$$\frac{n !}{s^{n+1}}, \quad s>0$$ \\    \hline
4.                      $$t^{p},\quad p>-1$$            &
$$\frac{\Gamma(p+1)}{s^{p+1}} \quad s>0$$
\\          \hline
5.                      $$\sin (a t)$$
& $$\frac{a}{s^{2}+a^{2}} \quad s>0$$
\\           \hline
6.                      $$\cos (a t)$$
& $$\frac{s}{s^{2}+a^{2}}, \quad s>0$$
\\           \hline
7.                      $$\sinh (a t)$$
& $$\frac{a}{s^{2}-a^{2}}, \quad s> a$$          \\               \hline
8.                      $$\cosh (a t)$$
& $$\frac{s}{s^{2}-a^{2}}, \quad s> a$$          \\               \hline
9.                      $$e^{a t} \sin b t$$                      & $$\frac{b}{(s-a)^{2}+b^{2}}, \quad s>a$$        \\               \hline
10.                     $$e^{a t}\cos (b t)$$                       & $$\frac{s-a}{(s-a)^{2}+b^{2}}, \quad s>a$$        \\               \hline
11.                     $$t^{n} e^{a t},\quad n=$$                       positive
integer     & $$\frac{n !}{(s-a)^{n+1}}, \quad s>a$$ \\ \hline
12.                     $$u_{c}(t)$$         & $$e^{-c s}F(s)$$
\\                         \hline
13.                     $$u_{c}(t) f(t-c)$$          & $$e^{-c s}F(s)$$                   \\                               \hline
14.                     $$e^{c t} f(t)$$
& $$F(s-c)$$               \\                               \hline
15.                     $$f(c t)$$              & $$\frac{1}{c} F\left(\frac{s}{c}\right), \quad c>0$$
\\           \hline
16.                     $$\int_{0}^{t} f(t-\tau) g(\tau)d \tau$$                        & $$F(s) G(s)$$      \\           \hline
17.                     $$\delta(t-c)$$           & $$e^{-c s}$$
\\                         \hline
18.                     $$f^{(n)}(t)$$       & $$s^{n} F(s)-s^{n-1} f(0)-\cdots-f^{(n-1)}(0)$$      \\
\hline
19.                     $$(-t)^{n} f(t)$$            & $$F^{(n)}(s)$$
\\                         \hline
\end{tabular}

It has a lot of unwanted space as in $$e^{a t}$$ how can I delete this
space in a convient way, whitespace-cleanup for example ignores this
space. Any ideas?

Regards

Uwe Brauer