DLMF:4.15.E3 (Q1665): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
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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.m2acdec
Property / Symbols used
 
Property / Symbols used: cosecant function / rank
 
Normal rank
Property / Symbols used: cosecant function / qualifier
 
Defining formula:

csc z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}

\csc@@{\NVar{z}}
Property / Symbols used: cosecant function / qualifier
 
xml-id: C4.S14.E5.m2abdec
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.m2aidec
Property / Symbols used
 
Property / Symbols used: secant function / rank
 
Normal rank
Property / Symbols used: secant function / qualifier
 
Defining formula:

sec z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}

\sec@@{\NVar{z}}
Property / Symbols used: secant function / qualifier
 
xml-id: C4.S14.E6.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11222 / rank
 
Normal rank
Property / Symbols used: Q11222 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11222 / qualifier
 
xml-id: C4.S1.XMD7.m1hdec

Latest revision as of 18:19, 1 January 2020

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English
DLMF:4.15.E3
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    Statements

    sec ( x + i y ) = csc ( x + 1 2 π + i y ) , 𝑥 𝑖 𝑦 𝑥 1 2 𝜋 𝑖 𝑦 {\displaystyle{\displaystyle\sec\left(x+iy\right)=\csc\left(x+\tfrac{1}{2}\pi+% iy\right),}}
    0 references
    DLMF:4.15.E3
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2acdec
    0 references
    csc z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    C4.S14.E5.m2abdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aidec
    0 references
    sec z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}
    C4.S14.E6.m2aadec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1ndec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C4.S1.XMD7.m1hdec
    0 references