Function bigErf

src/compute-engine/numerics/special-functions.ts:2705–2721

(ce: ComputeEngine, x: BigNum)

 * Reference: NIST DLMF 9.2, 9.4, 9.7
 */
export function airyBiPrime(x: number): number {
  if (!isFinite(x)) return NaN;

  if (x > 9) {
    // Bi′(x) ~ x^{1/4} e^{ξ}/√π Σ v_k/ξ^k  (DLMF 9.7.8)
    const xi = airyXi(x);
    const xiHi = xi[0];
    if (!Number.isFinite(xiHi)) return Infinity; // e^{ξ} overflows first
    let sum = 1;
    let t = 1; // u_k/ξ^k
    let prevAbs = Infinity;
    for (let k = 1; k <= 60; k++) {
      t *= airyURatio(k) / xiHi;
      const v = (t * (6 * k + 1)) / (1 - 6 * k); // v_k/ξ^k
      const av = Math.abs(v);
      if (av >= prevAbs) break; // divergent tail: stop at smallest term
      sum += v;
      prevAbs = av;
      if (av < 1e-18 * Math.abs(sum)) break;
    }