Proof step
Ray basis map theorem
Image under a basis map u^k -> P_k A008277
- Concludes
- one_plus_derivative of basis_map_A008277 of basis-map coefficients of A scaled Hermite triangle.
- Premises
- shift_x_plus_one of basis-map coefficients of A scaled Hermite triangle.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- shift_x_plus_one of basis-map coefficients of A scaled Hermite triangle.
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-b1d95225a770c834· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A008277", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-25618720f869b4747ac29e39a9c9a49c4c131673ff651ee9c8e1c545f6dc2e043f2, 7,565 bytes (1,502 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-60ff4e3f10bcffe9(real_rooted)n-60ff4e3f10bcffe9(one_signed_coefficients)n-60ff4e3f10bcffe9(hadamard_kernel)
References
- [MW08] Shi-Mei Ma and Yi Wang. q-Eulerian polynomials and polynomials with only real zeros. The Electronic Journal of Combinatorics, 15(1):Research Paper 17, January 2008. doi:10.37236/741