What is the infinitive of "can"?

Like the title says: I don't think "to can" is right :)

I mean "can" as in to be able to. I'm aware of other meanings.

I can't find the answer here. (There's What is an "infinitive"? which sidesteps this precise case). Online dictionaries draw a blank (http://www.merriam-webster.com/dictionary/can, e.g.).

I'm looking for some official indication that the infinitive doesn't exist for this irregular verb.

It would be nice if someone could share any information on how this has evolved to be the case.

Solution 1:

"Can" is a modal verb and doesn't have an infinitive

See "Defective verbs":

Defective verbs

The modal auxiliary verbs, can, may, shall, will and must are defective in that they do not have infinitives; so, one cannot say, *I want him to can do it, but rather must say, I want him to be able to do it. The periphrases to be able to, to have to and to be going to are generally used in these cases.

Solution 2:

The word "can," meaning to put in a can, has the infinitive "to can."

The modal verb "can," meaning to be able, is invariable and defective, the latter meaning it has no infinitive or participle forms.

Solution 3:

Not all verbs have infinitives. From Wikipedia:

Defective verbs

The modal auxiliary verbs, can, may, shall, will and must are defective in that they do not have infinitives; so, one cannot say, *I want him to can do it, but rather must say, I want him to be able to do it. The periphrases to be able to, to have to and to be going to are generally used in these cases.