Proof step e-1b98e7733a40a4e4

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 c5e0ee5395b0e0ed4c6215b8643939ef61d6d840059b7fb4f239db806dc8c134, 7,414 bytes (1,625 compressed); download JSON

Cited by

• n-fdb186db0412847e (real_rooted)
• n-fdb186db0412847e (one_signed_coefficients)
• n-fdb186db0412847e (hadamard_kernel)