[OS X TeX] \Cauchy-Principal-Value-Integral

[Bruno Voisin]

Le mercredi, 27 nov 2002, à 08:12 Europe/Paris, Steffen Lund Hokland a 
écrit :

> Does anybody know if there exist a symbol which consists of an 
> integral (\int} with a vetically centered horisontal bar. It's quite 
> common notation for the Cauchy Principal Value integral, but I can't 
> seem to find it in the Not So Short ... or Daly and Kopka: 'A Guide to 
> LaTeX.
>
> The alternative, I guess, is to make the d... thing my self....

Or to use this thing I've written:

\newlength{\intwidth}
\DeclareRobustCommand{\fpint}[2]
   {\mathop{%
      \text{%
        \settowidth{\intwidth}{$\int$}%
        \makebox[0pt][l]{\makebox[\intwidth]{$-$}}%
        $\int_{#1}^{#2}$}}}

It assumes the package amsmath is loaded, so that the command \text can 
be used. This \fpint (for "finite part integral") does not work exactly 
as \int, it takes the limits as arguments, as in \fpint{0}{\infty} 
replacing \int_0^\infty.

The TeXbook says, for such composite symbols, taking \notin as an 
example on p. 437 in Appendix F: "The definition of \notin in Appendix 
B indicates how similar symbols can be constructed". But in Appendix B, 
pp. 360-361 I never managed to understand how the construction works 
(especially \c at ncel).

The best solution would of course be special fonts including the 
symbol, such as the AMS negated symbol fonts. The finite part integral 
is indeed in MathML specification, at slot U02A0D, see:

http://www.w3.org/TR/MathML2/02A.html
http://www.w3.org/TR/MathML2/bycodes.html

It is also included in the font Esstix-Six, available at:

ftp://ftp.elsevier.nl/pub/styles/esstix/esstix.zip

But I'm not aware of any TeX macro package for accessing these fonts.

Michel Bovani (Michel, êtes-vous en ligne ?) did some work earlier this 
summer on a set of PostScript mathematical fonts for accompanying 
Utopia, and the principal value integral was part of this set.

Good luck,

Bruno Voisin




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