Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013610
- Concludes
- basis_map_A013610 of Exponential Riordan array [x*exp(x),x].
- Premises
- Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
- Triangle of denominators in Leibniz's Harmonic Triangle a(n,k), n >= 1, 1 <= k <= n.
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-b39addc203527233· 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" } } }{ "claim": "interlacing", "from_index": 2, "kind": "weak", "orientation": "unordered" }- Certificate
basis_map, SHA-2569b0081adef3338c7b3fe766ae4498670faabd8aeefc6d94755fd8ee26a8d09d7, 15,680 bytes (3,146 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-f52aae032f81ced6(hadamard_kernel)n-f52aae032f81ced6(interlacing)n-f52aae032f81ced6(real_rooted)n-f52aae032f81ced6(one_signed_coefficients)