Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- shift_x_plus_one of basis_map_A013609 of basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008…
- Premises
- basis_map_A007318 of Even-numbered rows of Pascal's triangle.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A007318 of Even-numbered rows of Pascal's triangle.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-666ec6ed045ae37a· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-256362088e80e800f3b77d3a80c0f9a8d73921dbac1623c60493f20c231b34e80d0, 6,877 bytes (1,395 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-23c9ebec99e56671(one_signed_coefficients)n-23c9ebec99e56671(hadamard_kernel)n-23c9ebec99e56671(real_rooted)