Path Finder – Can an alchemist create magical objects using his formula?

No, your formulas do not help you make magical objects.

(Except the potions, of course, since the alchemist has a class characteristic specifically to allow them to do it, but you already know).

First, the alchemist does not have a launcher level, and therefore can not normally acquire other object creation skills. The rules for the alchemist class are mentioned under alchemy:

The alchemist uses his level as the caster level to determine any effect based on the caster level.

Similar phrases appear in other parts of the class description, such as under Brew Potion. Such phrases make do not they appear in complete classes of spells, like the magician or the sorcerer, so it could be inferred that the alchemist does not have a level of caster. As such, alchemists can not satisfy the requirements of the launcher level for the creation of objects, a fact affirmed in this frequent question.

There are ways to avoid this limitation. You could do multi-classes in a spell casting class to earn pitcher levels. Or you can acquire the Master Craftsman feat, which grants limited access to the creation of magical items by allowing your ranks in a Craft skill or profession count as your caster level to acquire certain object creation skills.

Suppose you gained access to a feat of creating elements such as an alchemist. You can create items that do not require spells, such as +1 weapons or +1 armor. For many items, you can choose to ignore the prerequisites in exchange for increasing the production CD to 5 per prerequisite, and this includes spells. If you had to get a wand or cane or other spell activation item with a spell in your formula list, or a friend who could cast the spell you wanted, you could use it to fulfill the spell's prerequisite (alchemists can " Do not use parchments.) Or you might find another way to cast a spell, such as through the discovery of Spells.

But can you use your formulas to satisfy the spell requirement for magical items?

As correctly identified in the class description,

the alchemist does not cast spells,

Instead the alchemist creates extracts. Regarding the extracts:

In many ways, they behave like spells in the form of a potion …

An extract is "thrown" by drinking it, as if drinking a potion: the effects of an extract exactly duplicate the spell on which its formula is based

So an extract, the main means of alchemists to deliver spells, is almost identical to a potion. Let's now review what is needed to fulfill the spell requirements of creating magical objects:

A character who has prepared the spell (or who knows the spell, in the case of a sorcerer or bard) can provide a prerequisite for the spell, or by using a magical element to complete the spell or trigger or a similar ability to a spell. That produces the desired spell effect.

A potion is an element activated by use, not a spell ending element (eg, displacement) or spell activation (eg, wand, staff), so it does not qualify to provide a prerequisite spell. Since the extracts are like potions, the extracts do not qualify to create magical objects either.

However, although the alchemist is still quite poor in his ability to make magical objects, the discovery of Material Mastery assists them.

When spending an extract from the same school and level as a spell prerequisite when creating a magic item, only a -2 penalty is applied to ignore that requirement, instead of -5.

However, keep in mind that you do not have to use the same spell as you need, only one from the same school and level, so your specific formulas will not help you create magical items. It only needs to have any formula of the same level and school, and even then it does not satisfy the previous spell requirement, it only reduces the penalty by ignoring the previous requirement.