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DLMF:23.18.E5 - MaRDI portal

DLMF:23.18.E5 (Q8058)

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DLMF:23.18.E5
No description defined

    Statements

    DLMF defining formula
    Ξ· ⁑ ( π’œ ⁒ Ο„ ) = Ξ΅ ⁒ ( π’œ ) ⁒ ( - i ⁒ ( c ⁒ Ο„ + d ) ) 1 / 2 ⁒ Ξ· ⁑ ( Ο„ ) , Dedekind-modular-Eta π’œ 𝜏 πœ€ π’œ superscript 𝑖 𝑐 𝜏 𝑑 1 2 Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\mathcal{A}\tau\right)=\varepsilon(% \mathcal{A})\left(-i(c\tau+d)\right)^{1/2}\eta\left(\tau\right),}}
    0 references
    Symbols used
    Dedekind’s eta function (or Dedekind modular function)
    DLMF defining formula
    Ξ· ⁑ ( Ο„ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    xml-id
    C27.S14.E12.m2adec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    complex variable
    DLMF defining formula
    Ο„ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C23.S1.XMD9.m1cdec
    0 references
    Q12087
    DLMF defining formula
    π’œ π’œ {\displaystyle{\displaystyle\mathcal{A}}}
    xml-id
    C23.S15.XMD1.m1bdec
    0 references
    integer
    DLMF defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C23.S15.XMD4.m1dec
    0 references
    integer
    DLMF defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C23.S15.XMD5.m1dec
    0 references
    function
    DLMF defining formula
    Ξ΅ ⁒ ( π’œ ) πœ€ π’œ {\displaystyle{\displaystyle\varepsilon(\mathcal{A})}}
    xml-id
    C23.S18.XMD3.m1dec
    0 references

    Identifiers

     
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