Defining and calling function in one step

You can try:

(window.powers = function(i) {
  /*Code here*/
  alert('test : ' + i);
})(2);

<a href="#" onclick="powers(654)">Click</a>

Working link : http://jsfiddle.net/SqBp8/

It gets called on load, and I have added it to an anchor tag to change the parameter and alert.

If all you want is access the function within its own body, you can simply specify a name after the function keyword:

> (function fac (n) {
    return (n === 0 ? 1 : n*fac(n-1));
  })(10)
3628800

This is a standard feature (see ECMA-262, ed. 5.1, p. 98).

All the answers here are close to what you want, but have a few problems (adding it to the global scope, not actually calling it, etc). This combines a few examples on this page (although it unfortunately requires you to remember arguments.callee):

var test = (function() {
  alert('hi');
  return arguments.callee;
})();

Later, you can call it:

test();

If you don't care about the return value, you can do this.

var powers = function powers(i) {
    var product = i * i;
    console.log(i * i);
    if (product < 1e6) { powers(product) };
    return powers;
}(2);