Proof step e-cf285083c5135dab

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Triangle read by rows: T(n,k) = C(n+3,3) * C(n,k), 0 <= k <= n. JSON

Theorem

Gamma criterion RealRooted IsGammaExpansion.isRealRooted_and_hasRootsNonpos_iff ?

Operation

Gamma polynomial of a palindromic parent

{
  "index_shift": 0,
  "operation": "gamma_polynomial",
  "scale": "1"
}

Premises

• Triangle read by rows: T(n,k) = C(n+3,3) * C(n,k), 0 <= k <= n. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: gamma_polynomial, SHA-256 44d8461dc971485ec4fb5bfd6ab36c5f3d574fe78f1eedfe6e305bc6601a84cc, 9,820 bytes (2,249 compressed); download JSON

Cited by

• n-f71a45e9f51781db (real_rooted)
• n-f71a45e9f51781db (one_signed_coefficients)
• n-f71a45e9f51781db (hadamard_kernel)