DLMF:4.23.E18 (Q1770): 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.m2addec
Property / Symbols used
 
Property / Symbols used: arccotangent function / rank
 
Normal rank
Property / Symbols used: arccotangent function / qualifier
 
test:

arccot z 𝑧 {\displaystyle{\displaystyle\operatorname{arccot}\NVar{z}}}

\acot@@{\NVar{z}}
Property / Symbols used: arccotangent function / qualifier
 
xml-id: C4.S23.E9.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
test:

arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7acdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
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.m1rdec

Latest revision as of 17:31, 1 January 2020

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DLMF:4.23.E18
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    Statements

    arccot z = ± 1 2 π - arctan z , 𝑧 plus-or-minus 1 2 𝜋 𝑧 {\displaystyle{\displaystyle\operatorname{arccot}z=\pm\tfrac{1}{2}\pi-% \operatorname{arctan}z,}}
    0 references
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    z 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
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    arccot z 𝑧 {\displaystyle{\displaystyle\operatorname{arccot}\NVar{z}}}
    C4.S23.E9.m2acdec
    0 references
    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7acdec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1rdec
    0 references