Regarding 3rd definition:
var foo = function foo() { return 5; }
Heres an example which shows how to use possibility of recursive call:
a = function b(i) {
if (i>10) {
return i;
}
else {
return b(++i);
}
}
console.log(a(5)); // outputs 11
console.log(a(10)); // outputs 11
console.log(a(11)); // outputs 11
console.log(a(15)); // outputs 15
Edit: more interesting example with closures:
a = function(c) {
return function b(i){
if (i>c) {
return i;
}
return b(++i);
}
}
d = a(5);
console.log(d(3)); // outputs 6
console.log(d(8)); // outputs 8