Proof step e-5fbd3e16dd967779

basis_map A013609 → concludes about basis_map_A013609 of Riordan array ((1+x)^3,x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Riordan array ((1+x)^3,x). (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 197c3a77e8a2c68f127b4bed0c827b6aa1631de21b98694012fc3f57ac5aef57, 6,919 bytes (1,403 compressed); download JSON

Cited by

• n-48e70e0cceeb235f (real_rooted)
• n-48e70e0cceeb235f (one_signed_coefficients)
• n-48e70e0cceeb235f (hadamard_kernel)