Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- one_plus_derivative of Exponential Riordan array [x*exp(x),x].
- Premises
- one_plus_derivative of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- one_plus_derivative of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-f61fb736c5ac5680· 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-256cdfb5ad73645e1bc473991db4178e4a92169382968b8a7b834dd3277cc4aac84, 13,370 bytes (2,557 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-922a52ffa8f2e057(real_rooted)n-922a52ffa8f2e057(one_signed_coefficients)n-922a52ffa8f2e057(hadamard_kernel)