I've nothing to do with txfonts (more exactly, txmi family). Maybe you can use another Times like font package. mathptmx works fine (but it has fewer symbols than txfonts), and if you use XeTeX, you can also use XITS Math for math fonts. Commercial fonts like MathTimePro(2) are also good-looking.
I suggest XITS Math with XeLaTeX:
\documentclass{article}
\usepackage{unicode-math}
\setmainfont{XITS}
\setmathfont{XITS Math}
\begin{document}
See $S_1$, $S_2$, $S_3$.
\end{document}
\somefunction
I have remove \textit entirely. In math mode variables (a-zA-Zα-ο) are usually typeset in italic shape. Math mode takes care of the italic correction (between F and ( in this case).
If you want to use \somefunction in text, use always inline math (\(…\)).
It wouldn't be that wrong to use a simple definition for the entity (pd) and “fix” the spacing inside \somefunction (or better: entityFunction/\funcOfEnt/…) except when parenthesized entities will be used more often and outside of a function, like (\entity{pd} + \entity{qr}) x, than the definition of the function should use the already patched \entity to be more consistent.
\textit and \texttt
I don't think there is a total automatic solution available for fixing the problem with ) and following punctuation.
Let's take a look at the options:
\ittt
Your original \ittt was defined as
\newcommand*{\ittt}[1]{\textit{\texttt{#1}}}
\itttm
If you only use your entities in text mode before punctuation, \itttm can work for you. It adds italic correction only in math mode.
\newcommand*{\itttm}[1]{%
\ifmmode\mmodebeforetrue\else\mmodebeforefalse\fi%
\textit{\texttt{#1\ifmmodebefore\/\fi}}%
}
\itttp
The macro \itttp typsets a second optional parameter in italic shape (but not in the typewriter family). This has been discussed on TeX.SE already.
In my eyes, this is even too tight.
\DeclareDocumentCommand{\itttp}{m O{}}{%
\textit{\texttt{#1}#2\/}%
}
\ttit
Switching \textit and \texttt gives us italic correction. But it also adds this italic correction before punctuation mark where you don't want it (i.e., . and ,).
\newcommand*{\ttit}[1]{\texttt{\textit{#1}}}
\ttitc
Like \ttit, but:
The if-macro \@ifnextchar removes the italic correction before . and , with a negative kern.
I also tested both variants with \emph:
\emph{\texttt{pd}} is a little better before ), and as good as \ittt before punctuation\texttt{\emph{pd}} is as bad as \ttit.
\entity[*]{<arg>}
I also declared another macro: \entity. It does exist in a non-starred and a starred form.
Use the starred form if you do not want italic correction (i.e. before . and ,).
Conclusion
I think the best solutions are:
\itttm if you need italic correction only in math mode.\ttitc if can handle a few cases where the automatically inserted correction has to be re-corrected\entity if you're willing to use a switch (the *) to toggle italic correction (it should be doable to use \@ifnextchar in \entity, too).
Code
\documentclass{article}
\usepackage{times}
\usepackage{txfonts}
\usepackage{array,multirow,xcolor} % for presentation
\def\dont{\color[gray]{.5}} % *
\usepackage{xparse}% for \itttp and \entity
\newif\ifmmodebefore% for \itttm
\newcommand*{\somefunction}[1]{F(#1)}
\newcommand*{\ittt}[1]{\textit{\texttt{#1}}}
\newcommand*{\ttit}[1]{\texttt{\textit{#1}}}
\newcommand*{\itttm}[1]{% \itttc inserts italic correction \/ if in math mode
\ifmmode\mmodebeforetrue\else\mmodebeforefalse\fi%
\textit{\texttt{#1\ifmmodebefore\/\fi}}%
}
\makeatletter % needed because @ is used in macro name
\newcommand*{\ttitc}[1]{% \ttitc checks if . or , follows and kerns
\texttt{\textit{#1}}%
\@ifnextchar.{\kern-.1em}{\@ifnextchar,{\kern-.08em}{}}%
}
\makeatother
\DeclareDocumentCommand{\itttp}{m O{}}{% optional punctuation will be typeset italic
\textit{\texttt{#1}#2\/}%
}
\DeclareDocumentCommand{\entity}{s m}{% star = no italic correction (before , and .)
\textit{\texttt{#2}%
\IfBooleanTF{#1}%
{}%
{\/}%
}%
}
%\usepackage{lua-visual-debug} % use this with LuaLaTeX for debug-mode
\begin{document}\noindent
\begin{tabular}{l@{}c@{ }c@{ }c}
macro & math & \verb|\times| & text \\ \hline& text mode \\ \hline
\verb|\ittt{pd}| & $(\ittt{pd} )$ & $ \ittt{pd} \times {}$ & \ittt{pd}, \ittt{pd}. \\ \hline
\verb|\itttm{pd}| & $(\itttm{pd})$ & $ \itttm{pd} \times {}$ & \itttm{pd}, \itttm{pd}. \\
\verb|\itttp{pd}| & $(\itttp{pd})$ & $ \itttp{pd} \times {}$ & \dont \itttp{pd}, \itttp{pd}. \\
\verb|\itttp{pd}[.]| & --- & --- & \itttp{pd}[,] \itttp{pd}[.] \\ \hline
\verb|\ttit{pd}| & \multirow{2}{*}{$(\ttit{pd} )$} & \multirow{2}{*}{$ \ttit{pd} \times {}$} & \ttit{pd}, \ttit{pd}. \\
\verb|\ttitc{pd}| & & & \ttitc{pd}, \ttitc{pd}. \\ \hline
\verb|\entity{pd}| & $(\entity{pd})$ & $ \entity{pd} \times {}$ & \dont \entity{pd}, \entity{pd}. \\
\verb|\entity*{pd}| & --- & --- & \entity*{pd}, \entity*{pd}. \\
\end{tabular}
\end{document}
Output
Best Answer
The log shows
0 Italic correction
1 scriptspace
That is an empty subscript 0.5pt wide
2 (after)
A negative kern to back up after the subscript
3 (inside)
a zero width subscript (containing the negative kern)
So somewhat surprisingly I'd say that of the last two the most natural output is the last one which produces the empty subscript of zero width.
In this case with fx cases 2 and 3 with the italic correction supressed don't look good, but that isn't the point here.