DLMF:4.23.E33 (Q1785): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: general arctangent function / rank
 
Normal rank
Property / Symbols used: general arctangent function / qualifier
 
Defining formula:

Arctan z multivalued-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctan}\NVar{z}}}

\Atan@@{\NVar{z}}
Property / Symbols used: general arctangent function / qualifier
 
xml-id: C4.S23.E3.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11219 / rank
 
Normal rank
Property / Symbols used: Q11219 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11219 / qualifier
 
xml-id: C4.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1abdec

Latest revision as of 18:35, 1 January 2020

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DLMF:4.23.E33
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    Statements

    w = Arctan z = arctan z + k π , 𝑤 multivalued-inverse-tangent 𝑧 𝑧 𝑘 𝜋 {\displaystyle{\displaystyle w=\operatorname{Arctan}z=\operatorname{arctan}z+k% \pi,}}
    0 references
    DLMF:4.23.E33
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    z ± i 𝑧 plus-or-minus imaginary-unit {\displaystyle{\displaystyle z\neq\pm\mathrm{i}}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aldec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2amdec
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    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7afdec
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    Arctan z multivalued-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctan}\NVar{z}}}
    C4.S23.E3.m2abdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C4.S1.XMD1.m1bdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1abdec
    0 references