Function seriesResidue

test/compute-engine/series.test.ts:415–422

The residue (coefficient of `(x−x0)⁻¹`) extracted from the Series: the * constant term of `Series((x−x0)·f, x, x0, 0)`, which is `(x−x0)·f` evaluated * at the (removable) pole.

(fLatex: string, x0Latex: string)

  test('sqrt(1+x) to order 3: ascending degree starting with the constant term, O(x^4) last', () => {
    const latex = series('\\sqrt{1+x}', '0', 3).latex;
    expect(latex.startsWith('1+\\frac{x}{2}')).toBe(true);
    expect(latex).toBe(
      '1+\\frac{x}{2}-\\frac{x^2}{8}+\\frac{x^3}{16}+O\\left(x^4\\right)'
    );
  });

  test('arctan x at +infinity: descending degree, O(x^{-7}) last', () => {
    const latex = series('\\arctan x', '+\\infty').latex;
    expect(latex.startsWith('\\frac{\\pi}{2}-\\frac{1}{x}')).toBe(true);
    expect(latex).toBe(
      '\\frac{\\pi}{2}-\\frac{1}{x}+\\frac{1}{3x^3}-\\frac{1}{5x^5}+O\\left(\\frac{1}{x^7}\\right)'