DLMF:4.23.E41 (Q1793): Difference between revisions

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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.m1ldec

Latest revision as of 18:37, 1 January 2020

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DLMF:4.23.E41
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    Statements

    Defining formula
    gd - 1 ⁡ ( x ) = ∫ 0 x sec ⁡ t ⁢ d t , inverse-Gudermannian 𝑥 superscript subscript 0 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(x\right)=\int_{0}^{x% }\sec t\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:4.23.E41
    0 references
    constraint
    - 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}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    secant function
    Defining formula
    sec ⁡ z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}
    xml-id
    C4.S14.E6.m2adec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1ldec
    0 references
     
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