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DLMF:4.26.E5 - MaRDI portal

DLMF:4.26.E5 (Q2123)

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DLMF:4.26.E5
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    Statements

    DLMF defining formula
    ∫ 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),}}
    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}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    inverse Gudermannian function
    DLMF defining formula
    gd - 1 ⁡ ( x ) inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}
    xml-id
    C4.S23.E41.m2adec
    0 references
    secant function
    DLMF defining formula
    sec ⁡ z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}
    xml-id
    C4.S14.E6.m2adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1ddec
    0 references

    Identifiers

     
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