התמרת לפלס

function simpleResidues(poles) {
  if (new Set(poles).size !== poles.length) {
    throw new RangeError("simpleResidues requires distinct simple poles");
  }
  return poles.map((pole, k) => 1 / poles.reduce(
    (product, other, j) => j === k ? product : product*(pole-other),
    1
  ));
}

function inverseLaplace(t, poles, residues) {
  return residues.reduce(
    (sum, residue, k) => sum + residue*Math.exp(poles[k]*t),
    0
  );
}

const poles = [0, -1, -2];
const residues = simpleResidues(poles);
console.log(residues); // [0.5, -1, 0.5]
console.log([0, 1, 3].map(
  (t) => ({ t, y: inverseLaplace(t, poles, residues) })
));

from math import exp, prod

def simple_residues(poles):
    if len(set(poles)) != len(poles):
        raise ValueError("simple_residues requires distinct simple poles")
    return [
        1/prod(p-q for j, q in enumerate(poles) if j != k)
        for k, p in enumerate(poles)
    ]

def inverse_laplace(t, poles, residues):
    return sum(a*exp(p*t) for a, p in zip(residues, poles))

poles = [0, -1, -2]
residues = simple_residues(poles)
print(residues)
print([(t, inverse_laplace(t, poles, residues))
       for t in (0, 1, 3)])