DLMF:27.14.E14 (Q8113): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(7 intermediate revisions by the same user not shown)
Property / constraint
 

ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}

\imagpart@@{\tau}>0
Property / constraint: ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}} / rank
 
Normal rank
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
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
test:

ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q12267 / rank
 
Normal rank
Property / Symbols used: Q12267 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12267 / qualifier
 
xml-id: C27.S14.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12268 / rank
 
Normal rank
Property / Symbols used: Q12268 / qualifier
 
test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q12268 / qualifier
 
xml-id: C27.S14.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q12269 / rank
 
Normal rank
Property / Symbols used: Q12269 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q12269 / qualifier
 
xml-id: C27.S14.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q12270 / rank
 
Normal rank
Property / Symbols used: Q12270 / qualifier
 
test:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q12270 / qualifier
 
xml-id: C27.S14.XMD7.m1dec

Latest revision as of 13:31, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:27.14.E14
No description defined

    Statements

    test
    η ⁡ ( a ⁢ τ + b c ⁢ τ + d ) = ε ⁢ ( - i ⁢ ( c ⁢ τ + d ) ) 1 2 ⁢ η ⁡ ( τ ) , Dedekind-modular-Eta 𝑎 𝜏 𝑏 𝑐 𝜏 𝑑 𝜀 superscript imaginary-unit 𝑐 𝜏 𝑑 1 2 Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\frac{a\tau+b}{c\tau+d}\right)=% \varepsilon(-\mathrm{i}(c\tau+d))^{\frac{1}{2}}\eta\left(\tau\right),}}
    0 references
    DLMF id
    DLMF:27.14.E14
    0 references
    constraint
    ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
    0 references
    Symbols used
    Dedekind’s eta function (or Dedekind modular function)
    test
    η ⁡ ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    xml-id
    C27.S14.E12.m2abdec
    0 references
    Q10901
    test
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q12267
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C27.S14.XMD4.m1dec
    0 references
    Q12268
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C27.S14.XMD5.m1dec
    0 references
    Q12269
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C27.S14.XMD6.m1dec
    0 references
    Q12270
    test
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C27.S14.XMD7.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q8113&oldid=45802"