Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- Exponential Riordan array [x*exp(x),x].
- Premises
- Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-46cecb4caa3ed7bf· 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-256498bc98ed62170aa45d749a40eda79c5211e2b0c25bbe4dd82b929fe110d73f0, 12,660 bytes (2,494 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-308cf60736924b4c(real_rooted)n-308cf60736924b4c(one_signed_coefficients)n-308cf60736924b4c(hadamard_kernel)