DLMF:27.14.E13 (Q8112): Difference between revisions

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

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

\imagpart@@{\tau}>0
Property / constraint: 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.m2aadec
Property / Symbols used
 
Property / Symbols used: Euler’s reciprocal function / rank
 
Normal rank
Property / Symbols used: Euler’s reciprocal function / qualifier
 
test:

f ( x ) Euler-phi 𝑥 {\displaystyle{\displaystyle\mathit{f}\left(\NVar{x}\right)}}

\EulerPhi@{\NVar{x}}
Property / Symbols used: Euler’s reciprocal function / qualifier
 
xml-id: C27.S14.E2.m2acdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2aadec

Latest revision as of 13:31, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:27.14.E13
No description defined

    Statements

    η ( τ ) = e π i τ / 12 f ( e 2 π i τ ) . Dedekind-modular-Eta 𝜏 superscript 𝑒 imaginary-unit 𝜏 12 Euler-phi superscript 𝑒 2 imaginary-unit 𝜏 {\displaystyle{\displaystyle\eta\left(\tau\right)=e^{\pi\mathrm{i}\tau/12}% \mathit{f}\left(e^{2\pi\mathrm{i}\tau}\right).}}
    0 references
    0 references
    τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
    0 references
    η ( τ ) Dedekind-modular-Eta 𝜏 {\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}
    C27.S14.E12.m2aadec
    0 references
    f ( x ) Euler-phi 𝑥 {\displaystyle{\displaystyle\mathit{f}\left(\NVar{x}\right)}}
    C27.S14.E2.m2acdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2acdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
    0 references
    absent {\displaystyle{\displaystyle\Im}}
    C1.S9.E2.m2aadec
    0 references