lean_workbook_plus_43895

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Prove that the generating function $\sum_{k=0}^{\infty} 2^{2^k}x^k$ does not have a closed form for any $x \neq 0$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_43895 (x : ℝ) (hx : x ≠ 0) : ¬ ∃ f : ℝ → ℝ, f x = ∑' k : ℕ, 2^(2^k) * x^k   :=  by sorry

“No closed form” is replaced by nonexistence of any function taking a prescribed totalized-sum value.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Define the intended expression class if asking about closed forms. A concrete analytic task is to prove the power series has radius of convergence zero and diverges for every real x≠0.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.