DLMF:4.26.E3 (Q1819): Difference between revisions

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Property / constraint
 

- 1 2 π < x < 1 2 π 1 2 𝜋 𝑥 1 2 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi<x<\tfrac{1}{2}\pi}}

-\tfrac{1}{2}\pi<x<\tfrac{1}{2}\pi
Property / constraint: - 1 2 π < x < 1 2 π 1 2 𝜋 𝑥 1 2 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi<x<\tfrac{1}{2}\pi}} / rank
 
Normal rank
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: 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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
test:

tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1bdec

Latest revision as of 17:40, 1 January 2020

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DLMF:4.26.E3
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    Statements

    tan x d x = - ln ( cos x ) , 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\int\tan x\mathrm{d}x=-\ln\left(\cos x\right),}}
    0 references
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    - 1 2 π < x < 1 2 π 1 2 𝜋 𝑥 1 2 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi<x<\tfrac{1}{2}\pi}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2abdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2adec
    0 references
    tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    C4.S14.E4.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1bdec
    0 references