Proof step e-7b745496cf172799

basis_map A111125 → concludes about Riordan array (1+2x,x(1+x)). JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A111125",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Triangle of Stirling numbers of 2nd kind, S(n,k), n >= 0, 0 <= k <= n. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in [0, 1]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": true, "value": "-4" }, "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 4008d52c2220f13fe6acd5bbb218195fe367bfff0a8cdbd4f62c2ca957466c1f, 12,427 bytes (2,040 compressed); download JSON

Cited by

• n-c27b11147fce8bfa (real_rooted)
• n-c27b11147fce8bfa (one_signed_coefficients)
• n-c27b11147fce8bfa (hadamard_kernel)