Proof step e-313e6d9276f9a630

gamma_polynomial scale 1, shift 0 → concludes about Triangular array binomial(2*n-k, k), k=0..n, n >= 0. 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

• Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a triangle. (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 d72c29ea18c91554c274f815021f8f0dcd8fc6bf888721e810e3a4635d5c08e7, 10,287 bytes (2,330 compressed); download JSON

Cited by

• n-6758fe7729845be8 (one_signed_coefficients)
• n-6758fe7729845be8 (hadamard_kernel)
• n-6758fe7729845be8 (real_rooted)