Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013611 of Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order).
- Premises
- basis_map_A013609 of 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]
- basis_map_A013609 of 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-a664d1f27b976611· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "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-256829fa83e360a1ad61097f741b0d6a5cf5601f6573df3d0936da5761ef3b72b53, 13,480 bytes (2,557 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-a1e0668357b9b581(real_rooted)n-a1e0668357b9b581(one_signed_coefficients)n-a1e0668357b9b581(hadamard_kernel)n-a1e0668357b9b581(interlacing)