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I want to know how to add \vdots and \ddots to org-entities-user variable. This will display the values when I call org-entities-help

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Each element of org-entities-user is a list of 7 items which according to the manual are:

name                 As a string, without the leading backslash.
LaTeX replacement    In ready LaTeX, no further processing will take place.
LaTeX mathp          Either t or nil.  When t this entity needs to be in
                     math mode.
HTML replacement     In ready HTML, no further processing will take place.
                     Usually this will be an &...; entity.
ASCII replacement    Plain ASCII, no extensions.

Latin1 replacement   Use the special characters available in latin1.
utf-8 replacement    Use the special characters available in utf-8.

You add new entries like this:

(add-to-list 'org-entities-user
             '("vdots" "\\vdots{}" t "&x2999" "..." "..." "⁞"))

where the last four entries will vary based on what you want to display in html, ASCII, latin1 and utf8 respectivly. The t in the middle indicates that the \vdots Latex macro should be used in math mode.

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