Proof step e-023010f9acf2a31f

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Pascal-(1,8,1) array. 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

• Pascal-(1,8,1) array. (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 342bf13768780537b99ffb6b85f720622a62d3b9b08c7118e93e9041c444e3aa, 10,482 bytes (2,392 compressed); download JSON

Cited by

• n-e4013d25fc6715f3 (real_rooted)
• n-e4013d25fc6715f3 (one_signed_coefficients)
• n-e4013d25fc6715f3 (hadamard_kernel)