Proof step e-c98ee7dbfb9a2305

preserver_image reversal, shift 0 → concludes about reversal 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): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":1,\"first_degree\":0,\"step\":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": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 c1e97f5e71e148e343a88c6fe47cd7fe658939113acf1c980118e895e94c6517, 8,770 bytes (2,400 compressed); download JSON

Cited by

• n-7807fcac430a0b13 (real_rooted)
• n-7807fcac430a0b13 (one_signed_coefficients)
• n-7807fcac430a0b13 (hadamard_kernel)