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 Riordan array (1-x,x/(1-x)).
- Premises
- shift_x_plus_one of Riordan array (1-x,x/(1-x)).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- shift_x_plus_one of Riordan array (1-x,x/(1-x)).
- Theorem
- [MW08, Thm 2] polytool RealRooted rayBasisMap_maps_realRootedIn_iff ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-e1c5d532853b1a59· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A008277", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-25620ccce3460e4d622026ff18b5df08c7e38ee1db2f5c2511d5a6518b9ceca1604, 7,565 bytes (1,507 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-5d685a1643c9efb9(real_rooted)n-5d685a1643c9efb9(one_signed_coefficients)n-5d685a1643c9efb9(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