Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order).
- Premises
- A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-1b8c174a7adad0b1· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }{ "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-2566acd7c5d7b9fba8df8dadecab26184f91e750893629ba19baaf4ebccbf67c7ce, 13,480 bytes (2,555 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-30cb3cad216ed189(hadamard_kernel)n-30cb3cad216ed189(real_rooted)n-30cb3cad216ed189(interlacing)n-30cb3cad216ed189(one_signed_coefficients)