Execute the setInterval function without delay the first time

Here's a simple version for novices without all the messing around. It just declares the function, calls it, then starts the interval. That's it.

//Declare your function here
function My_Function(){
  console.log("foo");
}    

//Call the function first
My_Function();

//Set the interval
var interval = window.setInterval( My_Function, 500 );

For someone needs to bring the outer this inside as if it's an arrow function.

(function f() {
    this.emit("...");
    setTimeout(f.bind(this), 1000);
}).bind(this)();

If the above producing garbage bothers you, you can make a closure instead.

(that => {
    (function f() {
        that.emit("...");
        setTimeout(f, 1000);
    })();
})(this);

Or maybe consider using the @autobind decorator depending on your code.

You can set a very small initial delay-time (e.g. 100) and set it to your desired delay-time within the function:

var delay = 100;

function foo() {
  console.log("Change initial delay-time to what you want.");
  delay = 12000;
  setTimeout(foo, delay);
}

If you can use RxJS, there is something called timer():

import { Subscription, timer } from 'rxjs';

const INITIAL_DELAY = 1;
const INTERVAL_DELAY = 10000;
const timerSubscription = timer(INITIAL_DELAY, INTERVAL_DELAY)
  .subscribe(() => {
    this.updateSomething();
  });

// when destroying
timerSubscription.unsubscribe();

This example builds on @Alnitak's answer, but uses await Promise for finer granularity of control within the loop cycle.

Compare examples:

let stillGoing = true;

(function foo() {
    console.log('The quick brown fox did its thing');
    if (stillGoing) setTimeout(foo, 5000);
})();

foo();

In the above example we call foo() and then it calls itself every 5 seconds.

But if, at some point in the future, we set stillGoing to false in order to stop the loop, we'll still get an extra log line even after we've issued the stop order. This is because at any given time, before we set stillGoing to false the current iteration will have already created a timeout to call the next iteration.

If we instead use await Promise as the delay mechanism then we have an opportunity to stop the loop before calling the next iteration:

let stillGoing = true;

(async function foo() {
    console.log('The quick brown fox did its thing');
    await new Promise(resolve => setTimeout(resolve, 5000));
    if (stillGoing) foo();
})();

foo();

In the second example we start by setting a 5000ms delay, after which we check the stillGoing value and decide whether calling another recursion is appropriate.

So if we set stillGoing to false at any point, there won't be that one extra log line printed after we set the value.

The caveat is this requires the function to be async, which may or may not be an option for a given use.