DLMF:23.10.E15 (Q7313): Difference between revisions

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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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
Defining formula:

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2adec
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: Q12066 / rank
 
Normal rank
Property / Symbols used: Q12066 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12066 / qualifier
 
xml-id: C23.S1.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q12060 / rank
 
Normal rank
Property / Symbols used: Q12060 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12060 / qualifier
 
xml-id: C23.S1.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12049 / rank
 
Normal rank
Property / Symbols used: Q12049 / qualifier
 
Defining formula:

ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}

\omega_{1}
Property / Symbols used: Q12049 / qualifier
 
xml-id: C23.S1.XMD8.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12079 / rank
 
Normal rank
Property / Symbols used: Q12079 / qualifier
 
Defining formula:

A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}

A_{n}
Property / Symbols used: Q12079 / qualifier
 
xml-id: C23.S10.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12080 / rank
 
Normal rank
Property / Symbols used: Q12080 / qualifier
 
Defining formula:

G 𝐺 {\displaystyle{\displaystyle G}}

G
Property / Symbols used: Q12080 / qualifier
 
xml-id: C23.S10.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12059 / rank
 
Normal rank
Property / Symbols used: Q12059 / qualifier
 
Defining formula:

η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}

\eta_{j}
Property / Symbols used: Q12059 / qualifier
 
xml-id: C23.S2.XMD6.m1bdec

Latest revision as of 16:00, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:23.10.E15
No description defined

    Statements

    Defining formula
    A n = ( π 2 ⁢ G 2 ω 1 ) n 2 - 1 ⁢ q n ⁢ ( n - 1 ) / 2 i n - 1 ⁢ exp ⁡ ( - ( n - 1 ) ⁢ η 1 3 ⁢ ω 1 ⁢ ( ( 2 ⁢ n - 1 ) ⁢ ( ω 1 2 + ω 3 2 ) + 3 ⁢ ( n - 1 ) ⁢ ω 1 ⁢ ω 3 ) ) , subscript 𝐴 𝑛 superscript superscript 𝜋 2 superscript 𝐺 2 subscript 𝜔 1 superscript 𝑛 2 1 superscript 𝑞 𝑛 𝑛 1 2 superscript 𝑖 𝑛 1 𝑛 1 subscript 𝜂 1 3 subscript 𝜔 1 2 𝑛 1 superscript subscript 𝜔 1 2 superscript subscript 𝜔 3 2 3 𝑛 1 subscript 𝜔 1 subscript 𝜔 3 {\displaystyle{\displaystyle A_{n}=\left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right% )^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp\left(-\frac{(n-1)\eta_{1}}{3\omega% _{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}% \right)\right),}}
    0 references
    DLMF id
    DLMF:23.10.E15
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1dec
    0 references
    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1ddec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1ddec
    0 references
    Q12079
    Defining formula
    A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}
    xml-id
    C23.S10.XMD2.m1bdec
    0 references
    Q12080
    Defining formula
    G 𝐺 {\displaystyle{\displaystyle G}}
    xml-id
    C23.S10.XMD3.m1dec
    0 references
    Q12059
    Defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C23.S2.XMD6.m1bdec
    0 references
     
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