Proof step e-7ab50ded9e353f77

basis_map A007318 → concludes about basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j. (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 47531526f45891458f4227d22e2bd4c21dc4e8646c72955542eb43cc753ecfd6, 6,857 bytes (1,388 compressed); download JSON

Cited by

• n-7d034d48b0ca9aab (real_rooted)
• n-7d034d48b0ca9aab (one_signed_coefficients)
• n-7d034d48b0ca9aab (hadamard_kernel)