DLMF:20.2.E6 (Q6746): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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

Revision as of 14:29, 2 January 2020

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DLMF:20.2.E6
No description defined

    Statements

    Defining formula
    θ 1 ⁡ ( z + ( m + n ⁢ τ ) ⁢ π | τ ) = ( - 1 ) m + n ⁢ q - n 2 ⁢ e - 2 ⁢ i ⁢ n ⁢ z ⁢ θ 1 ⁡ ( z | τ ) , Jacobi-theta-tau 1 𝑧 𝑚 𝑛 𝜏 𝜋 𝜏 superscript 1 𝑚 𝑛 superscript 𝑞 superscript 𝑛 2 superscript 𝑒 2 𝑖 𝑛 𝑧 Jacobi-theta-tau 1 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{1}\left(z+(m+n\tau)\pi\middle|\tau\right)=% (-1)^{m+n}q^{-n^{2}}e^{-2inz}\theta_{1}\left(z\middle|\tau\right),}}
    0 references
    DLMF id
    DLMF:20.2.E6
    0 references
    Symbols used
    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.SS1.m1addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
     
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