If you'd like to simply open a fancybox when a javascript function is called. Perhaps in your code flow and not as a result of a click. Here's how you do it:

function openFancybox() {
  $.fancybox({
     'autoScale': true,
     'transitionIn': 'elastic',
     'transitionOut': 'elastic',
     'speedIn': 500,
     'speedOut': 300,
     'autoDimensions': true,
     'centerOnScroll': true,
     'href' : '#contentdiv'
  });
}

This creates the box using "contentdiv" and opens it.

Since you're using jQuery, stop binding event handlers in your HTML, and start writing unobtrusive JavaScript.

$(document).ready(function ()
{
    function myfunction(me)
    {
        $(me).fancybox({
            'autoScale': true,
            'transitionIn': 'elastic',
            'transitionOut': 'elastic',
            'speedIn': 500,
            'speedOut': 300,
            'autoDimensions': true,
            'centerOnScroll': true // remove the trailing comma!!
        }).click();
        // fire the click event after initializing fancybox on this element
        // this should open the fancybox
    }

    // use .one() so that the handler is executed at most once per element
    $('a[href=#modalMine]').one('click', function ()
    {
        myfunction(this);
        return false;
    });
});

However, I don't particularly see a reason for setting up the fancybox on click. You could just do this instead:

$(document).ready(function ()
{
    function myfunction()
    {
        // note the use of "this" rather than a function argument
        $(this).fancybox({
            'autoScale': true,
            'transitionIn': 'elastic',
            'transitionOut': 'elastic',
            'speedIn': 500,
            'speedOut': 300,
            'autoDimensions': true,
            'centerOnScroll': true
        });
    }

    $('a[href=#modalMine]').each(myfunction);
});

Basic demo (no images) →

What you need is:

$.fancybox.open({ .... });

See the "API methods" section at the bottom of here:

http://fancyapps.com/fancybox/