Proof step e-d66a62e99e497f2a

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Exponential Riordan array [x*exp(x),x]. 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": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

• Exponential Riordan array [x*exp(x),x]. (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": "-1" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 983b98274328e51fd8a6243fe3f9fa7c3f5f591ed82860b63c09268a3ad8f21c, 9,295 bytes (2,699 compressed); download JSON

Cited by

• n-7c4e320f16a7ccb1 (real_rooted)
• n-7c4e320f16a7ccb1 (one_signed_coefficients)
• n-7c4e320f16a7ccb1 (hadamard_kernel)