Proof step e-5f6cf10d49e0d311

preserver_image affine, shift 0 → concludes about basis_map_A007318 of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(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

• basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x). (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 311c33788ffcf717e0e9193fac61b35ffa986debe6300624db239b13cc713331, 8,592 bytes (2,358 compressed); download JSON

Cited by

• n-a75ac50997f70dee (one_signed_coefficients)
• n-a75ac50997f70dee (hadamard_kernel)
• n-a75ac50997f70dee (real_rooted)