DLMF:20.13.E5 (Q6855): 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.m2aadec

Revision as of 14:45, 2 January 2020

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DLMF:20.13.E5
No description defined

    Statements

    Defining formula
    π 4 ⁢ α ⁢ t ⁢ ∑ n = - ∞ ∞ ( - 1 ) n ⁢ e - ( n ⁢ π + z ) 2 / ( 4 ⁢ α ⁢ t ) = θ 4 ⁡ ( z | i ⁢ 4 ⁢ α ⁢ t / π ) . 𝜋 4 𝛼 𝑡 superscript subscript 𝑛 superscript 1 𝑛 superscript 𝑒 superscript 𝑛 𝜋 𝑧 2 4 𝛼 𝑡 Jacobi-theta-tau 4 𝑧 𝑖 4 𝛼 𝑡 𝜋 {\displaystyle{\displaystyle\sqrt{\frac{\pi}{4\alpha t}}\sum\limits_{n=-\infty% }^{\infty}(-1)^{n}e^{-(n\pi+z)^{2}/(4\alpha t)}=\theta_{4}\left(z\middle|i4% \alpha t/\pi\right).}}
    0 references
    DLMF id
    DLMF:20.13.E5
    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.m1aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
     
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