Proof step e-5048ce3ebd740a6f

basis_map A007318 → concludes about basis_map_A007318 of Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). (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": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 74df768afc942180b736cff615f9276c1ddf676929fd6ef6b47a8ee8cee483fa, 7,419 bytes (1,623 compressed); download JSON

Cited by

• n-03ac40ba4fd62e4c (real_rooted)
• n-03ac40ba4fd62e4c (one_signed_coefficients)
• n-03ac40ba4fd62e4c (hadamard_kernel)