Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of basis_map_A013609 of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downwa…
- Premises
- basis_map_A013609 of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downwa…
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013609 of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downwa…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-8fbc593398ab91d6· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-2560553127a52a9f4d085e19aa434a9697fead31676d676425a3c8ed1c401aa6605, 6,865 bytes (1,392 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-800c644c27747b67(one_signed_coefficients)n-800c644c27747b67(hadamard_kernel)n-800c644c27747b67(real_rooted)