Proof step e-de35ff8f60015c8a

basis_map A007318 → 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

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

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: basis_map, SHA-256 aedc247b5e5f393fa79b163779e60ea97ddf56024e6aab777743cbacb6277465, 7,413 bytes (1,621 compressed); download JSON

Cited by

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