Can you purchase legendaries from vending machines?

In the games current state it is not possible to get legendaries in a vending machine. It is possible however, to get legendaries out of the golden chest.

Edit: I forgot, it is possible to get a legendary in the "item of the day -slot" or whatever it is called but i dont have any rates.

Legendary Items can be Sold

On some rare chances, Legendary Items can be sold as the Item of the Day. >These will cost a lot more money so you might need to farm for them.

Source : https://gamewith.net/borderlands-3/article/show/11415

I’ve seen people say they’ve bought them from machines, but I’ve yet to see it. I’m level 53, and I haven’t seen them in regular machines, or the one right outside Earl’s door. I’ve also never received one in the golden key chest either. I’ve only ever picked them up as loot.

Edit: well, as of today with the new update, things have changed. Both machines in Sanctuary have legendaries for sale now. Yay!!

You can currently due to a short timed event that is currently going on. There is only one per machine.

https://borderlands.com/en-US/news/2020-03-26-borderlands-legendary-collection/

However, as mentioned in the comments, the loot tables change all the time.

Legendary items are now occasionally available in vending machines. They can show up as the "item of the day" and regular items. Mayhem levels are applied as well, as you can see in the screenshots. This was a change added with the 7/23/2020 patch which states:

Legendary Gear available in Vending Machines

We have rebalanced vending machines based on community feedback. Vending machines of all types have a small chance of providing Legendary gear for purchase.

Previously, legendaries were available during special events like the Door Busters mini-event that ran from 3/27/2020 to 4/2/2020 which enabled legendaries to be reliably found in most vending machines. Here is an example of two legendaries in one machine: a Techspert and a Big Boom Blaster