Proof step e-e169cb33ba7b2c8c

basis_map A013609 → concludes about basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^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 d70efd3cd775ddbfefd0ca5ab89198ed25d168c5a895b1c4e276560a908868f6, 6,859 bytes (1,394 compressed); download JSON

Cited by

• n-4f44de8e265280a7 (real_rooted)
• n-4f44de8e265280a7 (one_signed_coefficients)
• n-4f44de8e265280a7 (hadamard_kernel)