Function p4

test/compute-engine/special-functions.test.ts:1453–1460

(c: any)

// arguments). Both build on erf(z) = 1 − Γ(1/2, z²)/√π via
// incompleteGammaUpperComplex, reflected into the right half-plane (erf odd),
// with erfi(z) = −i·erf(i·z). Accuracy tracks that kernel (≲1e-12 for
// small/moderate |z|, degrading toward ~1e-7 in the large-|z| asymptotic
// region). Reference values from mpmath (dps=25).
describe('COMPLEX-ARGUMENT Erf, Erfi', () => {
  const expectComplex = (expr: any, re: number, im: number, tol = 1e-11) => {
    const v = expr.N();
    const scale = Math.hypot(re, im) * tol + tol;
    expect(Math.abs(v.re - re)).toBeLessThan(scale);
    expect(Math.abs(v.im - im)).toBeLessThan(scale);
  };
  const z = (re: number, im: number): any => ['Complex', re, im];