Proof step e-551d764375152d3c

basis_map A013611 → concludes about basis_map_A013611 of Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^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)*10^(i-j)*1^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 7d1d9fadcb60bfe5408e6e35da1587e534e320d30a26cf0f5c815178c6382948, 6,860 bytes (1,387 compressed); download JSON

Cited by

• n-e03395d80bc5749d (one_signed_coefficients)
• n-e03395d80bc5749d (hadamard_kernel)
• n-e03395d80bc5749d (real_rooted)