Proof step e-e8c658beda6fb788

basis_map A013611 → concludes about basis_map_A013609 of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Tr… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• binomial (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 bf5e7b76ca180ae378d8a15317a6e59928f6bfbabd0b3615f152c69f5fb9f355, 6,855 bytes (1,386 compressed); download JSON

Cited by

• n-465e4344a8d94925 (one_signed_coefficients)
• n-465e4344a8d94925 (hadamard_kernel)
• n-465e4344a8d94925 (real_rooted)