Proof step e-2d1052dd37eda11b

basis_map A013610 → concludes about basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,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 4c5778bc0c3174e8388323c5b8893b73d5d6eb5c11de3843b2e9cf1c79f18886, 6,855 bytes (1,390 compressed); download JSON

Cited by

• n-7f05fd9e9c6948d8 (real_rooted)
• n-7f05fd9e9c6948d8 (one_signed_coefficients)
• n-7f05fd9e9c6948d8 (hadamard_kernel)