Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- derivative of Exponential Riordan array [x*exp(x),x].
- Premises
- derivative of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- derivative of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-be234a5994111545· 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" } } }- Certificate
basis_map, SHA-256fd4f43123d5c7e1e9eea3d79a32e0680ce86c741db0632121c148b7f1cb8f87f, 13,518 bytes (2,616 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-4330f616ae0ed2bc(real_rooted)n-4330f616ae0ed2bc(one_signed_coefficients)n-4330f616ae0ed2bc(hadamard_kernel)