Proof step e-5f70bba9f74a761e

basis_map A060821 → concludes about Triangle read by rows. T(n, k) are the coefficients of the Hermite polynomial of order n, for 0 <= k <= n. JSON

Theorem

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

Operation

Image under a basis map u^k -> P_k

{
  "map": "A060821",
  "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 b5e854c485fcb260c4273ee077af6ef706a6969fd16c76559b276b2dbea9b4ae, 6,403 bytes (1,331 compressed); download JSON

Cited by

• n-95fc06ddb38bf951 (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