WordPress wp_title blank on index page

But if you use a static home page, this is the code:

<title><?php bloginfo('name'); ?> &raquo; <?php is_front_page() ? bloginfo('description') : wp_title(''); ?></title>

Here's is what I read from Codex:

If you are using a custom homepage with custom loops and stuff, you will have an empty wp_title. Here goes a neat hack to add the description/tagline at the wp_title place on homepage:

<title><?php bloginfo('name'); ?> | <?php is_front_page() ? bloginfo('description') : wp_title(''); ?></title>

So use is_front_page() to get the title on homepage, the way it is suggested in above code.

Update for WordPress versions (>= 4.4)

Try this

function some_name(){
    add_theme_support( 'title-tag' );
}

add_action( 'after_setup_theme', 'some_name' );

Do this in functions.php and remove 'title' tag from head...