Create an Org file with a link to an existing PDF file.  For example:

[[file:~/circulant_diagonalization.pdf][file:~/circulant_diagonalization.pdf]]

(assuming the mentioned file exists at that path).  In an attempt to open the
PDF in the system viewer, position point over the link and type
C-u C-u C-c C-o.

The link opens in DocView, belying the docstring, which says:
    With a double prefix argument, try to open outside of Emacs, in the
    application the system uses for this file type.

I reproduced with an empty Emacs init file.  I use Ubuntu 16.04.  The default
PDF application is Okular.

Emacs  : GNU Emacs 25.0.93.1 (x86_64-unknown-linux-gnu, GTK+ Version 3.18.9)
 of 2016-04-22
Package: Org-mode version 8.3.4 (8.3.4-39-ge0acd8-elpaplus @
/home/jorge/.emacs.d/elpa/org-plus-contrib-20160418/)

current state:
==============
(setq
 org-tab-first-hook '(org-hide-block-toggle-maybe org-babel-hide-result-
toggle-maybe org-babel-header-arg-expand)
 org-speed-command-hook '(org-speed-command-default-hook org-babel-speed-
command-hook)
 org-occur-hook '(org-first-headline-recenter)
 org-metaup-hook '(org-babel-load-in-session-maybe)
 org-confirm-shell-link-function 'yes-or-no-p
 org-after-todo-state-change-hook '(org-clock-out-if-current)
 org-src-mode-hook '(org-src-babel-configure-edit-buffer org-src-mode-
configure-edit-buffer)
 org-agenda-before-write-hook '(org-agenda-add-entry-text)
 org-babel-pre-tangle-hook '(save-buffer)
 org-mode-hook '(#[nil "\300\301\302\303\304$\207" [org-add-hook change-major-
mode-hook org-show-block-all append local] 5]
                 #[nil "\300\301\302\303\304$\207" [org-add-hook change-major-
mode-hook org-babel-show-result-all append local] 5]
                 org-babel-result-hide-spec org-babel-hide-all-hashes org-
eldoc-load)
 org-archive-hook '(org-attach-archive-delete-maybe)
 org-ctrl-c-ctrl-c-hook '(org-babel-hash-at-point org-babel-execute-safely-
maybe)
 org-cycle-hook '(org-cycle-hide-archived-subtrees org-cycle-hide-drawers org-
cycle-show-empty-lines
                  org-optimize-window-after-visibility-change)
 org-confirm-elisp-link-function 'yes-or-no-p
 org-metadown-hook '(org-babel-pop-to-session-maybe)
 org-clock-out-hook '(org-clock-remove-empty-clock-drawer)
 )

-- 
- I am Brazilian.  I hope my English is correct and I welcome corrections.
- Please adopt free formats like PDF, ODF, LaTeX, Vorbis, Opus, WebM and 7z.
- Free software for Android: https://f-droid.org/




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