リーマンゼータ関数の特殊値
ζ ( − 3 ) = 1 120 {\displaystyle \zeta (-3)={\frac {1}{120}}}
ζ ( − 5 ) = − 1 252 {\displaystyle \zeta (-5)=-{\frac {1}{252}}}
ζ ( − 7 ) = 1 240 {\displaystyle \zeta (-7)={\frac {1}{240}}}
ζ ( − 9 ) = − 1 132 {\displaystyle \zeta (-9)=-{\frac {1}{132}}}
ζ ( − 11 ) = 691 32760 {\displaystyle \zeta (-11)={\frac {691}{32760}}}
ζ ( − 13 ) = − 1 12 {\displaystyle \zeta (-13)=-{\frac {1}{12}}}
ζ ( − 15 ) = 3617 8160 {\displaystyle \zeta (-15)={\frac {3617}{8160}}}
ζ ( − 17 ) = − 43867 14364 {\displaystyle \zeta (-17)=-{\frac {43867}{14364}}}
ζ ( − 19 ) = 174611 6600 {\displaystyle \zeta (-19)={\frac {174611}{6600}}}
となる。特に ζ (−1) はラマヌジャン総和法(英語版)に関連する。