Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of basis_map_A013611 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_A013611 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_A013611 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-b0412fa6ae8da4ef· 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-25665dd40c61def3d0a1c2519ba568cb67a8455173d8ac1850a27c0f16236c99e90, 6,855 bytes (1,389 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-a041f87d41cb6b7b(one_signed_coefficients)n-a041f87d41cb6b7b(hadamard_kernel)n-a041f87d41cb6b7b(real_rooted)