DLMF:23.18.E6 (Q7366): 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
 
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.m2adec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
test:

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
 
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: Q12084 / rank
 
Normal rank
Property / Symbols used: Q12084 / qualifier
 
test:

𝒜 𝒜 {\displaystyle{\displaystyle\mathcal{A}}}

\mathcal{A}
Property / Symbols used: Q12084 / qualifier
 
xml-id: C23.S15.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12085 / rank
 
Normal rank
Property / Symbols used: Q12085 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12085 / qualifier
 
xml-id: C23.S15.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12087 / rank
 
Normal rank
Property / Symbols used: Q12087 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q12087 / qualifier
 
xml-id: C23.S15.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q12088 / rank
 
Normal rank
Property / Symbols used: Q12088 / qualifier
 
test:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q12088 / qualifier
 
xml-id: C23.S15.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q12092 / rank
 
Normal rank
Property / Symbols used: Q12092 / qualifier
 
test:

ε ( 𝒜 ) 𝜀 𝒜 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})}}

\varepsilon(\mathcal{A})
Property / Symbols used: Q12092 / qualifier
 
xml-id: C23.S18.XMD3.m1adec

Latest revision as of 00:20, 2 January 2020

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DLMF:23.18.E6
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    Statements

    ε ( 𝒜 ) = exp ( π i ( a + d 12 c + s ( - d , c ) ) ) , 𝜀 𝒜 𝜋 𝑖 𝑎 𝑑 12 𝑐 𝑠 𝑑 𝑐 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})=\exp\left(\pi i\left(% \frac{a+d}{12c}+s(-d,c)\right)\right),}}
    0 references
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references
    𝒜 𝒜 {\displaystyle{\displaystyle\mathcal{A}}}
    C23.S15.XMD1.m1cdec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C23.S15.XMD2.m1dec
    0 references
    c 𝑐 {\displaystyle{\displaystyle c}}
    C23.S15.XMD4.m1adec
    0 references
    d 𝑑 {\displaystyle{\displaystyle d}}
    C23.S15.XMD5.m1adec
    0 references
    ε ( 𝒜 ) 𝜀 𝒜 {\displaystyle{\displaystyle\varepsilon(\mathcal{A})}}
    C23.S18.XMD3.m1adec
    0 references