Proof step e-70e9e46985bbe802

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Triangle read by rows: T(n,k) = binomial(n+4,4) * binomial(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) = binomial(n+4,4) * binomial(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 6faf4e27bd4ab87f260f44a02b135e4d37155b0c2f894ec5bd4863c58b712666, 9,834 bytes (2,252 compressed); download JSON

Cited by

• n-0d90c938f81b41a4 (real_rooted)
• n-0d90c938f81b41a4 (one_signed_coefficients)
• n-0d90c938f81b41a4 (hadamard_kernel)