Proof step e-9c08db68889738c4

basis_map A013611 → concludes about basis_map_A013611 of Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k). 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 (n,k)-th entry is 15^(n-k)*binomial(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: basis_map, SHA-256 0304737e43fddbcbaf85d7d2853417b5bf90739017476db7c80a0157a8fa5501, 6,860 bytes (1,389 compressed); download JSON

Cited by

• n-21b46279e9abe0a4 (real_rooted)
• n-21b46279e9abe0a4 (one_signed_coefficients)
• n-21b46279e9abe0a4 (hadamard_kernel)