DLMF:27.14.E12 (Q8111): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: Dedekind’s eta function (or Dedekind modular function) / rank
 
Normal rank
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: 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.m2abdec
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.m2aadec
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.m2adec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1gdec

Latest revision as of 13:31, 2 January 2020

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English
DLMF:27.14.E12
No description defined

    Statements

    test
    η ⁡ ( τ ) = e π ⁢ i ⁢ τ / 12 ⁢ ∏ n = 1 ∞ ( 1 - e 2 ⁢ π ⁢ i ⁢ n ⁢ τ ) , Dedekind-modular-Eta 𝜏 superscript 𝑒 imaginary-unit 𝜏 12 superscript subscript product 𝑛 1 1 superscript 𝑒 2 imaginary-unit 𝑛 𝜏 {\displaystyle{\displaystyle\eta\left(\tau\right)=e^{\pi\mathrm{i}\tau/12}% \prod_{n=1}^{\infty}(1-e^{2\pi\mathrm{i}n\tau}),}}
    0 references
    DLMF id
    DLMF:27.14.E12
    0 references
    constraint
    ℑ ⁡ τ > 0 𝜏 0 {\displaystyle{\displaystyle\Im\tau>0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q10901
    test
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q12234
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1gdec
    0 references
     
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