Proof step e-b3e711c86f592bbc

basis_map A013609 → concludes about basis_map_A013609 of Exponential Riordan array (1, x(1+x/2)). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Exponential Riordan array (1, x(1+x/2)). (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 7d8523508d2287a212108cb4c905510006365f016e48118041b19c41a41958de, 11,708 bytes (2,210 compressed); download JSON

Cited by

• n-f771467984d796d1 (real_rooted)
• n-f771467984d796d1 (one_signed_coefficients)
• n-f771467984d796d1 (hadamard_kernel)