Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- basis_map_A013610 of theta_plus_one of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).
- Premises
- theta_plus_one of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- theta_plus_one of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-5ab27899a6afac50· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013610", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-256f3ed2d7444eeb5133ef1ee3281123404fe165b86e6e5334fbf458f3da87f6621, 7,647 bytes (1,703 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-ef3d39adbae9d30c(real_rooted)n-ef3d39adbae9d30c(one_signed_coefficients)n-ef3d39adbae9d30c(hadamard_kernel)