Proof step e-c5d35f047ff7eb16

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of eulerian 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

• eulerian (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 364bfcd3dfd35d86a8cdeb049140d32eb09ca57aa9b77a470a0999aadb700f1a, 6,631 bytes (1,887 compressed); download JSON

Cited by

• n-0942305fd4723770 (real_rooted)
• n-0942305fd4723770 (one_signed_coefficients)
• n-0942305fd4723770 (hadamard_kernel)