Proof step e-8b7786e9ad6af8fd

gamma_polynomial scale 1/4, shift 0 → concludes about peak JSON

Theorem

Gamma criterion RealRooted IsGammaExpansion.isRealRooted_and_hasRootsNonpos_iff ?

Operation

Gamma polynomial of a palindromic parent

{
  "index_shift": 0,
  "operation": "gamma_polynomial",
  "scale": "1/4"
}

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 31ee916f2bc2b782427e46536eed99cb314fbe1c4a2bd24e5e3c239bddff99c7, 7,266 bytes (2,078 compressed); download JSON

Cited by

• n-92480a234eee36bb (real_rooted)
• n-92480a234eee36bb (one_signed_coefficients)
• n-92480a234eee36bb (hadamard_kernel)