Proof step e-b31a65521e9db5ca

basis_map A066325 → concludes about hermite_he JSON

Theorem

Hermite-type basis map [MW08, Thm 2] polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A066325",
  "operation": "basis_map"
}

Premises

• a(n) = 1 if n is of the form m(m+3)/2, otherwise 0. (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": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 76b5925bbc7e2b1e038d1026fdc2790316f8c06bd756a5c2ca9e9f9d91b99b2e, 6,403 bytes (1,325 compressed); download JSON

Cited by

• n-b0b0e9fb10acb2e2 (real_rooted)

References

1. [MW08] Shi-Mei Ma and Yi Wang. q-Eulerian polynomials and polynomials with only real zeros. The Electronic Journal of Combinatorics, 15(1):Research Paper 17, January 2008. doi:10.37236/741