What's the convention nowdays? The reference book I am using (which is pretty old btw) goes [math]a_1+\cfrac{b_1}{a_2+\cfrac{b_2}{a_3+\cfrac{b_3}{a_4+\ldots}}}[/math]

While the online resources goes a_0,b_1,a_1,b_2...

Also which one is more conventional [math][a_1;a_2,a_3][/math] or [math][a_1,a_2,a_3][/math]

I know it doesnt matter, but I just wanna stick to the standards.

I was made to accept the [a1,a2,a3]

The latter.

In my course, we used the notation [imath]a_0,a_1,a_2,a_3,\dots[/imath] - the advantage being, that for periodic continued fractions, we could simply represent it as: [imath]a_0, a_1, a_2, \overline{a_3, a_4, a_5}[/imath].

erm yeah but my main question was wheter to start the sequence from a_0 or a_1, i guess if everyone is doing it from a_0, I should as well.

Sorry, I didn't realise that was the question

 

I would probably start from a₀ as well.