@Michael has there been any progress on this?

Using version 6.1.0 for mac

plot(1:10)
title('\varphi and \phi')

Look the same.

I have had a look what symbols TeX supports [1] and are not currently implemented in Octave [2]. From those I've picked the ones I personally have seen in scientific plots and consider them useful myself. So here is my suggested (and maybe very personal) list:

*** My personal wish list: ***
\varepsilon  (useful and common for any kind of formulas)
\varrho      (useful and common for any kind of formulas)
\varphi      (useful and common for any kind of formulas)
\hbar        (useful for Physics stuff)
\sqrt        (is this doable without excessiv effort?)
\sum         (but there is already \Sigma)
\prod        (but there is already \Pi)
\ominus      (because there is already \oplus in Octave)
\odot        (because there is already \otimes in Octave)
\ll          (this looks more professional as <<)
\gg          (this looks more professional as >>)
\parallel    (because there is already \perp in Octave)
\simeq       (currently there is only \sim in Octave)
\notin       (currently there seem to be no negationas at all in Octave, except for \neq)
\not=        (even if there is already \neq in Octave)
\Leftrightarrow      (currently there is only \leftrightarrow in Octave)
\mapsto      (useful arrow type for Math)
\rightleftharpoons   (useful for chemical stuff)
\Uparrow     (currently there is only \uparrow in Octave)
\Downarrow   (currently there is only \uparrow in Octave)

(alternate names for already existing TeX symbols in Octave:)
\le
\ge
\to
\gets
\owns
\land
\lor
\lnot

[1] http://www.math.union.edu/~dpvc/jsmath/symbols/welcome.html
This webpage claims to list „The symbols listed in Appendix F of The TeXbook“

[2] https://www.gnu.org/software/octave/doc/interpreter/Use-of-the-interpreter-Property.html

Here is the full list of TeX symbols in [1] which are not yet in Octave [2] (leftout stuff is marked with square brackets):

*** Full list of possibly missing TeX symbols ***
Greek Letters
\varepsilon
\varrho
\varphi


Symbols of type Ord
\hbar
\imath
\jmath
\ell
\emptyset     (there is alreaddy \O )
\top
\bot
\|
\triangle      (there is already \Delta )
\backslash
\flat
\natural
\sharp

\cdots
\vdots
\ddots


Functions
[…]
\sqrt        (is this doable without excessiv effort?)
\root 3\of


"Large" Operators
\sum       (but there is already \Sigma)
\prod      (but there is already \Pi)
\coprod
\oint
\bigcap
\bigcup
\bigsqcup
\bigvee
\bigwedge
\bigodot
\bigotimes
\bigoplus
\biguplu


Binary operations
\mp
\setminus
\star
\diamond
\uplus
\sqcap
\sqcup
\triangleleft
\triangleright
\wr
\bigcirc
\bigtriangleup
\bigtriangledown
\ominus      (because there is already \oplus in Octave)
\odot        (because there is already \otimes in Octave)
\dagger
\ddagger
\amalg


Relations and their Negations
\prec
\preceq
\ll         (this looks more professional as <<)
\sqsubseteq
\vdash
\smile
\frown
\succ
\succeq
\gg         (this looks more professional as >>)
\sqsupseteq
\dashv
\parallel   (because there is already \perp in Octave)
\simeq      (currently there is only \sim in Octave)
\asymp
\bowtie
\models
\doteq

\not<
\not\leq
\not\preceq
\not\subset
\not\subseteq
\not\sqsubseteq
\not>
\not\geq
\not\succ
\not\succeq
\not\supset
\not\supseteq
\not\sqsupseteq
\notin        (currently there seem to be no negationas at all in Octave, except for \neq)
\not=         (even if there is already \neq in Octave)
\not\equiv
\not\sim
\not\simeq
\not\approx
\not\cong
\not\asymp


Arrows
\Leftrightarrow   (currently there is only \leftrightarrow in Octave)
\mapsto           (useful arrow type for Math)
\hookleftarrow
\leftharpoonup
\leftharpoondown
\rightleftharpoons   (useful for chemical stuff)
\longleftarrow
\Longleftarrow
\longrightarrow
\Longrightarrow
\longleftrightarrow
\Longleftrightarrow
\longmapsto
\hookrightarrow
\rightharpoonup
\rightharpoondown
\Uparrow            (currently there is only \uparrow in Octave)
\Downarrow          (currently there is only \uparrow in Octave)
\updownarrow
\Updownarrow
\nearrow
\searrow
\swarrow
nwarrow


Delimiters
[…]

Matrices and Arrays
[…]

Alternate Names and Non-Math Symbols
\le
\ge
\{
\}
\to
\gets
\owns
\land
\lor
\lnot
|
\|
\dagger
\ddagger

Given that we like to view Octave as a superset of Matlab, I don't have an issue with adding some more symbols to the list.  But, I don't want to go overboard and add 1,000 new entries.

Would someone be willing to look at TeX and the Octave manual and come up with a list of additional symbols that would be useful?

Table 15.1 is actually derived from the TeX Book.

I think that it is a good idea to adher to what is specified
by Knuth in his documentation.

There are other means of introducing TeX source code,
as explained in the Manual.

This was discussed about a year ago when Table 15.1 and
the code were updated to match the tables in the TeX Book.

Oh, sorry. Then I was mislead by the information in the mentioned book of jwe on "Octave 3" (link in my original post). Maybe that's a bit outdated now.

If those symbols currently are not mentioned in the Octave manual nor support by Matlab, then I personally wouldn't consider this to be a bug at all.

But now it's up to the TeX experts...

Here is some sample script to show what I mean:

close all;
graphics_toolkit('fltk');
%graphics_toolkit('gnuplot');
plot(1:10);
r = 'works: \alpha \approx \leftrightarrow ';
s = ', works not: \varphi \Leftrightarrow \Uparrow \Downarrow \notin \prod \diamond ';
t = '\bigrightriangledown';
title([r,s,t]);

If I run this on Octave 3.8.1 as well as on Octave 3.8.2-rc1 under Ubuntu Linux, then the TeX symbols in s and t are NOT shown on screen. This is using FLTK.

If I switch to Gnuplot, then most of those symbols appear on screen, just the one in t still does not appear.

I assumed that all of those symbols should work because of this reference: www.network-theory.co.uk/docs/octave3/octave_172.html

I don't know if this happens as well on Windows installations, but I would assume yes.