DLMF:23.18.E5 (Q7365): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Dedekind’s eta function (or Dedekind modular function) / rank
 
Normal rank
Property / Symbols used: Dedekind’s eta function (or Dedekind modular function) / qualifier
 
Defining formula:

η ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}

\Dedekindeta@{\NVar{\tau}}
Property / Symbols used: Dedekind’s eta function (or Dedekind modular function) / qualifier
 
xml-id: C27.S14.E12.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12068 / rank
 
Normal rank
Property / Symbols used: Q12068 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: Q12068 / qualifier
 
xml-id: C23.S1.XMD9.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12084 / rank
 
Normal rank
Property / Symbols used: Q12084 / qualifier
 
Defining formula:

𝒜 𝒜 {\displaystyle{\displaystyle\mathcal{A}}}

\mathcal{A}
Property / Symbols used: Q12084 / qualifier
 
xml-id: C23.S15.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12087 / rank
 
Normal rank
Property / Symbols used: Q12087 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q12087 / qualifier
 
xml-id: C23.S15.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12088 / rank
 
Normal rank
Property / Symbols used: Q12088 / qualifier
 
Defining formula:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q12088 / qualifier
 
xml-id: C23.S15.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q12092 / rank
 
Normal rank
Property / Symbols used: Q12092 / qualifier
 
Defining formula:

ε ( 𝒜 ) 𝜀 𝒜 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})}}

\varepsilon(\mathcal{A})
Property / Symbols used: Q12092 / qualifier
 
xml-id: C23.S18.XMD3.m1dec

Latest revision as of 01:20, 2 January 2020

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DLMF:23.18.E5
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    Statements

    η ( 𝒜 τ ) = ε ( 𝒜 ) ( - i ( c τ + d ) ) 1 / 2 η ( τ ) , Dedekind-modular-Eta 𝒜 𝜏 𝜀 𝒜 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
    DLMF:23.18.E5
    0 references
    η ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    C27.S14.E12.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    C23.S1.XMD9.m1cdec
    0 references
    𝒜 𝒜 {\displaystyle{\displaystyle\mathcal{A}}}
    C23.S15.XMD1.m1bdec
    0 references
    c 𝑐 {\displaystyle{\displaystyle c}}
    C23.S15.XMD4.m1dec
    0 references
    d 𝑑 {\displaystyle{\displaystyle d}}
    C23.S15.XMD5.m1dec
    0 references
    ε ( 𝒜 ) 𝜀 𝒜 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})}}
    C23.S18.XMD3.m1dec
    0 references