Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of theta_plus_one_squared of basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array …
- Premises
- theta_plus_one_squared of basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array …
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- theta_plus_one_squared of basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array …
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-a40bb3707b858dd7· 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-256bfbe3055027d9ce7f14327e7de0c256743bca303223ba591a8e6d5da140003e3, 11,452 bytes (2,041 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-149dd9466dcf24f9(one_signed_coefficients)n-149dd9466dcf24f9(hadamard_kernel)n-149dd9466dcf24f9(real_rooted)