4.21 Identities4.23 Inverse Trigonometric Functions

§4.22 Infinite Products and Partial Fractions

4.22.1 \mathop{\sin\/}\nolimits z=z\prod _{{n=1}}^{\infty}\left(1-\frac{z^{2}}{n^{2}\pi^{2}}\right),
4.22.2 \mathop{\cos\/}\nolimits z=\prod _{{n=1}}^{\infty}\left(1-\frac{4z^{2}}{(2n-1)^{2}\pi^{2}}\right).

When z\neq n\pi, n\in\Integer,

4.22.3 \mathop{\cot\/}\nolimits z=\frac{1}{z}+2z\sum _{{n=1}}^{\infty}\frac{1}{z^{2}-n^{2}\pi^{2}},
4.22.4 {\mathop{\csc\/}\nolimits^{{2}}}z=\sum _{{n=-\infty}}^{\infty}\frac{1}{(z-n\pi)^{2}},
4.22.5 \mathop{\csc\/}\nolimits z=\frac{1}{z}+2z\sum _{{n=1}}^{\infty}\frac{(-1)^{n}}{z^{2}-n^{2}\pi^{2}}.