sinz1=cotz+tan(z/2)
πtan(πz)=8zn=0∑∞(2n+1)2−4z21
πcot(πz)=z1+2zn=1∑∞z2−n21
sin(πz)π=z1+2z[n=1∑∞z2−n21−n=0∑∞z2−(2n+1)21]=
=z1+2z[z2−121+z2−221+z2−321+...−z2−122−z2−122−z2−122−...]=
=z1+n=1∑∞(−1)n−1n2−z22z
cos(πz)=sin(π(1/2−z))
cos(πz)1=π[1−2z2+(1+2z2−3−2z2)−(3+2z2−5−2z2)+...]=
=π[12−4z24⋅1−32−4z24⋅3+52−4z24⋅5−...]
=4πn=0∑∞(−1)n(2n+1)2−4z22n+1
if z = 0, tnen:
π/4=1−1/3+1/5−1/7+...
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