DLMF:4.26.E5 (Q1821): 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: 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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
Property / Symbols used
 
Property / Symbols used: inverse Gudermannian function / rank
 
Normal rank
Property / Symbols used: inverse Gudermannian function / qualifier
 
Defining formula:

gd - 1 ( x ) inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}

\aGudermannian@{\NVar{x}}
Property / Symbols used: inverse Gudermannian function / qualifier
 
xml-id: C4.S23.E41.m2adec
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.m2adec
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.m1ddec

Latest revision as of 18:40, 1 January 2020

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DLMF:4.26.E5
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    Statements

    sec x d x = gd - 1 ( x ) , 𝑥 𝑥 inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle\int\sec x\mathrm{d}x={\operatorname{gd}^{-1}}% \left(x\right),}}
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    DLMF:4.26.E5
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    - 1 2 π < x < 1 2 π 1 2 𝜋 𝑥 1 2 𝜋 {\displaystyle{\displaystyle-\frac{1}{2}\pi<x<\frac{1}{2}\pi}}
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1addec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3addec
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    gd - 1 ( x ) inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}
    C4.S23.E41.m2adec
    0 references
    sec z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}
    C4.S14.E6.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1ddec
    0 references