DLMF:20.13.E4 (Q6854): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
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
Property / Symbols used
 
Property / Symbols used: Q11947 / rank
 
Normal rank
Property / Symbols used: Q11947 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11947 / qualifier
 
xml-id: C20.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11957 / rank
 
Normal rank
Property / Symbols used: Q11957 / qualifier
 
Defining formula:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q11957 / qualifier
 
xml-id: C20.S13.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11958 / rank
 
Normal rank
Property / Symbols used: Q11958 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q11958 / qualifier
 
xml-id: C20.S13.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11956 / rank
 
Normal rank
Property / Symbols used: Q11956 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11956 / qualifier
 
xml-id: C20.S13.XMD3.m1cdec

Latest revision as of 14:45, 2 January 2020

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DLMF:20.13.E4
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    Statements

    π 4 α t n = - e - ( n π + z ) 2 / ( 4 α t ) = θ 3 ( z | i 4 α t / π ) , 𝜋 4 𝛼 𝑡 superscript subscript 𝑛 superscript 𝑒 superscript 𝑛 𝜋 𝑧 2 4 𝛼 𝑡 Jacobi-theta-tau 3 𝑧 𝑖 4 𝛼 𝑡 𝜋 {\displaystyle{\displaystyle\sqrt{\frac{\pi}{4\alpha t}}\sum\limits_{n=-\infty% }^{\infty}e^{-(n\pi+z)^{2}/(4\alpha t)}=\theta_{3}\left(z\middle|i4\alpha t/% \pi\right),}}
    0 references
    DLMF:20.13.E4
    0 references
    θ j ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    C20.S2.SS1.m1adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C20.S1.XMD2.m1dec
    0 references
    t 𝑡 {\displaystyle{\displaystyle t}}
    C20.S13.XMD1.m1bdec
    0 references
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    C20.S13.XMD2.m1bdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C20.S13.XMD3.m1cdec
    0 references