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 Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2).
- Premises
- basis_map_A007318 of Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A007318 of Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2).
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-921714fc9366b500· 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-2561f42f77f0a7b9dcfe3309bf0b73f334b7ca8f4f5d644f177ce33cec04033cfae, 9,053 bytes (1,955 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-eaae521881f3a9f9(real_rooted)n-eaae521881f3a9f9(one_signed_coefficients)n-eaae521881f3a9f9(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