Proof step e-9c6e37fd70f39446

preserver_image affine, shift -1 → concludes about Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": -1,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"-1\"}"
}

Premises

• hermite_he (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)

Claims

• { "claim": "real_rooted", "from_index": 1, "region": {} }
• { "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 7f81dc997268c8d25cadc1232f018af6480b41ff66fe1dda376b115c8b6cbe54, 12,753 bytes (2,697 compressed); download JSON

Cited by

• n-f0c4b6406e0da4a3 (real_rooted)
• n-f0c4b6406e0da4a3 (interlacing)