Function expectNumericNearPole

test/compute-engine/series.test.ts:426–440

Assert `Normal(Series(f, x, x0, n))` matches `f` numerically at points near * the pole, within a relative tolerance.

(
  poly: BoxedExpression,
  f: (x: number) => number,
  x0: number,
  dxs: number[],
  relTol: number
)

    expect(latex).toBe(
      '\\frac{\\pi}{2}-\\frac{1}{x}+\\frac{1}{3x^3}-\\frac{1}{5x^5}+O\\left(\\frac{1}{x^7}\\right)'
    );
  });

  test('a BigO-free sum is unaffected (canonical order preserved)', () => {
    // Regression guard: the display-order rule only applies to sums that
    // actually contain a `BigO` term.
    expect(ce.parse('x^5 - x^3 + x').latex).toBe('x^5-x^3+x');
  });

  test('AsciiMath uses ascending degree with BigO last', () => {
    expect(toAsciiMath(series('\\sin x'))).toBe(
      'x - 1/6 * x^3 + 1/120 * x^5 + BigO(x^7)'
    );
  });

  test('AsciiMath uses descending degree for an expansion at infinity', () => {
    expect(toAsciiMath(series('\\arctan x', '+\\infty'))).toBe(
      '1/2 * pi - 1 / x + 1/3 * x^(-3) - 1/5 * x^(-5) + BigO(x^(-7))'