Proof step e-9171c77362f53bc9

gamma_polynomial scale 1, shift 0 → concludes about gamma_polynomial of Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). 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

• Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). (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 8569f69b68d9831e43aca6a6fac85493d53850dce1878195971e1c900e13381e, 5,328 bytes (1,561 compressed); download JSON

Cited by

• n-7c6e1d5e4a537ecf (real_rooted)
• n-7c6e1d5e4a537ecf (one_signed_coefficients)
• n-7c6e1d5e4a537ecf (hadamard_kernel)