Proof step e-62a1b0a86f60f435

basis_map A013611 → concludes about basis_map_A013611 of Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j. (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: basis_map, SHA-256 5f6c4d3068c3fffafd2c22fbfcd53bd7f8b9d97c0187b6f1badafbc5175b2587, 6,859 bytes (1,394 compressed); download JSON

Cited by

• n-384c17a53af3442c (real_rooted)
• n-384c17a53af3442c (one_signed_coefficients)
• n-384c17a53af3442c (hadamard_kernel)