Proof step e-941e1ded9756e612

preserver_image derivative_of_power_multiple, shift 0 → concludes about Expansion of the rotational partition function for a heteronuclear diatomic molecule. JSON

Theorem

Rolle’s theorem (elementary) polytool ?

Lean (RealRooted): route derivativeXMul RealRooted.DegreeDropReversal.splits_X_pow_mul_iff, Polynomial.Splits.iterate_derivative

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"derivative_of_power_multiple\",\"power\":1,\"derivative_order\":1}"
}

Premises

• a(n) = 1 if n is a triangular number, otherwise 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 37fa516d810ad8e49ffd5e1e0eefa711a9aca0836a30e3a04b8746082cb51a73, 6,437 bytes (1,731 compressed); download JSON

Cited by

• n-6299862621ff8810 (real_rooted)
• n-6299862621ff8810 (one_signed_coefficients)
• n-6299862621ff8810 (hadamard_kernel)