Proof step e-69d63c555e6a484b

basis_map A013610 → concludes about basis_map_A007318 of Triangle of coefficients in expansion of (2+3x)^n. 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 binomial(i,j)*4^(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 b19a0104a38446fda5fd5faed2f4166695548012d17ee7a7d98ad1048ecd04fe, 6,855 bytes (1,390 compressed); download JSON

Cited by

• n-05c39cd3844b146d (real_rooted)
• n-05c39cd3844b146d (one_signed_coefficients)
• n-05c39cd3844b146d (hadamard_kernel)