Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- derivative of Even-numbered rows of Pascal's triangle.
- Premises
- derivative of basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) re…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- derivative of basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) re…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-cf8568343e28676f· 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-2561ba7f8c242e7c6e74da26714cd6d4aa26428f1870ad93d18a57d1c5d6287b7bb, 11,767 bytes (2,134 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-f1591709bf5cf41b(real_rooted)n-f1591709bf5cf41b(one_signed_coefficients)n-f1591709bf5cf41b(hadamard_kernel)