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4 Elementary FunctionsTrigonometric Functions

§4.22 Infinite Products and Partial Fractions

4.22.1 sinz =zn=1(1z2n2π2),
4.22.2 cosz =n=1(14z2(2n1)2π2).

When znπ, n,

4.22.3 cotz =1z+2zn=11z2n2π2,
4.22.4 csc2z =n=1(znπ)2,
4.22.5 cscz =1z+2zn=1(1)nz2n2π2.