Hi !

it is an "infinite power tower"

But your symbolism is ambiguous : it could means several different power towers. One have to use brakets to give a precise definition (in attachment)

If the tower is finite (with a finit number of x), the related function of x can be formally expressed as the first derivative of a Generalized Sophomores Dream function : Formula 12:5 in the paper "The Sophomores Dream Function"

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