DLMF:23.19.E2 (Q7369): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Klein’s complete invariant / rank
 
Normal rank
Property / Symbols used: Klein’s complete invariant / qualifier
 
Defining formula:

J ⁡ ( τ ) Kleins-invariant-modular-J 𝜏 {\displaystyle{\displaystyle J\left(\NVar{\tau}\right)}}

\KleincompinvarJtau@{\NVar{\tau}}
Property / Symbols used: Klein’s complete invariant / qualifier
 
xml-id: C23.S15.E7.m2adec
Property / Symbols used
 
Property / Symbols used: elliptic modular function / rank
 
Normal rank
Property / Symbols used: elliptic modular function / qualifier
 
Defining formula:

λ ⁡ ( τ ) modular-Lambda 𝜏 {\displaystyle{\displaystyle\lambda\left(\NVar{\tau}\right)}}

\modularlambdatau@{\NVar{\tau}}
Property / Symbols used: elliptic modular function / qualifier
 
xml-id: C23.S15.E6.m2aadec
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.m1adec

Latest revision as of 01:20, 2 January 2020

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DLMF:23.19.E2
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    Statements

    Defining formula
    J ⁡ ( τ ) = 4 27 ⁢ ( 1 - λ ⁡ ( τ ) + λ 2 ⁡ ( τ ) ) 3 ( λ ⁡ ( τ ) ⁢ ( 1 - λ ⁡ ( τ ) ) ) 2 , Kleins-invariant-modular-J 𝜏 4 27 superscript 1 modular-Lambda 𝜏 modular-Lambda 2 𝜏 3 superscript modular-Lambda 𝜏 1 modular-Lambda 𝜏 2 {\displaystyle{\displaystyle J\left(\tau\right)=\frac{4}{27}\frac{\left(1-% \lambda\left(\tau\right)+{\lambda^{2}}\left(\tau\right)\right)^{3}}{\left(% \lambda\left(\tau\right)\left(1-\lambda\left(\tau\right)\right)\right)^{2}},}}
    0 references
    DLMF id
    DLMF:23.19.E2
    0 references
    Symbols used
    Klein’s complete invariant
    Defining formula
    J ⁡ ( τ ) Kleins-invariant-modular-J 𝜏 {\displaystyle{\displaystyle J\left(\NVar{\tau}\right)}}
    xml-id
    C23.S15.E7.m2adec
    0 references
    elliptic modular function
    Defining formula
    λ ⁡ ( τ ) modular-Lambda 𝜏 {\displaystyle{\displaystyle\lambda\left(\NVar{\tau}\right)}}
    xml-id
    C23.S15.E6.m2aadec
    0 references
    Q12068
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C23.S1.XMD9.m1adec
    0 references
     
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