Bennett Gamma add two

Proved

D1Bound5.bennett_Gamma_add_two

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result bennett_Gamma_add_two in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring

Formal statement

section
namespace D1Bound5



theorem _root_.D1Bound5.bennett_Gamma_add_two (x : ℝ) (hx : 0 < x) :
    Real.Gamma (x + 2) = (x + 1) * x * Real.Gamma x := by sorry

















end D1Bound5
end

Source

D1Bound5/BennettTwoBetaBound.lean, lines 17-21, SHA-256 6be0ec4b4373f2704cbfdc6beb52a3796d8063f1c67fa2c91242af5752323182. Project: https://github.com/tomislav-math/d1-bound5-lean

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