Proof step e-e643036831fc9f95

basis_map A007318 → concludes about basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^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 6098f7e90ccf29cf653edea14d60eee084c3abc2353684d77bdd89babfcdb86f, 6,909 bytes (1,409 compressed); download JSON

Cited by

• n-809ca598570cd420 (real_rooted)
• n-809ca598570cd420 (one_signed_coefficients)
• n-809ca598570cd420 (hadamard_kernel)