Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A013609
- Concludes
- basis_map_A013609 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-6004bea62902fff7· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A013609", "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-256ec2fcf7352519e21315ce833d3ae73fab4b890421b0bc24f8d735210c2714f83, 15,678 bytes (3,144 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-93a9da031f1ee988(interlacing)n-93a9da031f1ee988(real_rooted)n-93a9da031f1ee988(one_signed_coefficients)n-93a9da031f1ee988(hadamard_kernel)