DLMF:4.14.E3 (Q1655): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1bdec

Latest revision as of 17:18, 1 January 2020

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DLMF:4.14.E3
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    Statements

    cos z ± i sin z = e ± i z , plus-or-minus 𝑧 𝑖 𝑧 superscript 𝑒 plus-or-minus 𝑖 𝑧 {\displaystyle{\displaystyle\cos z\pm i\sin z=e^{\pm iz},}}
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1bdec
    0 references