Proof step e-d0b0c6817e15c3a8

basis_map A007318 → concludes about basis_map_A007318 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": "A007318",
  "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 93468e2d25d96efa93eeabfc4f759506dde54fa65692011a064bb921152130c7, 11,708 bytes (2,205 compressed); download JSON

Cited by

• n-11e2e791fe8625e3 (real_rooted)
• n-11e2e791fe8625e3 (one_signed_coefficients)
• n-11e2e791fe8625e3 (hadamard_kernel)