Proof step e-8792ddb513a0c57e

basis_map A007318 → concludes about basis_map_A007318 of Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2). (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 acbfc6e681c99122b47261877f69d55f4aaafb13366256d1e5128109f314969a, 7,414 bytes (1,622 compressed); download JSON

Cited by

• n-be3f02dc425ece52 (real_rooted)
• n-be3f02dc425ece52 (one_signed_coefficients)
• n-be3f02dc425ece52 (hadamard_kernel)