DLMF:25.6.E19 (Q7656)

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DLMF:25.6.E19
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    test
    ( m + n + 3 2 ) ⁢ ζ ⁡ ( 2 ⁢ m + 2 ⁢ n + 2 ) = ( ∑ k = 1 m + ∑ k = 1 n ) ⁢ ζ ⁡ ( 2 ⁢ k ) ⁢ ζ ⁡ ( 2 ⁢ m + 2 ⁢ n + 2 - 2 ⁢ k ) , 𝑚 𝑛 3 2 Riemann-zeta 2 𝑚 2 𝑛 2 superscript subscript 𝑘 1 𝑚 superscript subscript 𝑘 1 𝑛 Riemann-zeta 2 𝑘 Riemann-zeta 2 𝑚 2 𝑛 2 2 𝑘 {\displaystyle{\displaystyle\left(m+n+\tfrac{3}{2}\right)\zeta\left(2m+2n+2% \right)=\left(\sum_{k=1}^{m}+\sum_{k=1}^{n}\right)\zeta\left(2k\right)\zeta% \left(2m+2n+2-2k\right),}}
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    DLMF:25.6.E19
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