DLMF:27.14.E19 (Q8118)

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DLMF:27.14.E19
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    Statements

    Defining formula
    τ ⁡ ( m ) ⁢ τ ⁡ ( n ) = ∑ d | ( m , n ) d 11 ⁢ τ ⁡ ( m ⁢ n d 2 ) , Ramanujan-tau 𝑚 Ramanujan-tau 𝑛 subscript divides 𝑑 𝑚 𝑛 superscript 𝑑 11 Ramanujan-tau 𝑚 𝑛 superscript 𝑑 2 {\displaystyle{\displaystyle\tau\left(m\right)\tau\left(n\right)=\sum_{d% \mathbin{|}\left(m,n\right)}d^{11}\tau\left(\frac{mn}{d^{2}}\right),}}
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    DLMF id
    DLMF:27.14.E19
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    constraint
    m , n = 1 , 2 , … formulae-sequence 𝑚 𝑛 1 2 … {\displaystyle{\displaystyle m,n=1,2,\dots}}
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    Symbols used
    Ramanujan’s tau function
    Defining formula
    τ ⁡ ( n ) Ramanujan-tau 𝑛 {\displaystyle{\displaystyle\tau\left(\NVar{n}\right)}}
    xml-id
    C27.S14.E18.m2aadec
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    Q12093
    Defining formula
    ( m , n ) 𝑚 𝑛 {\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}
    xml-id
    C27.S1.p2.t1.r3.m6aadec
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    Q12239
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1adec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1jdec
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