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DLMF:4.23.E39 - MaRDI portal

DLMF:4.23.E39 (Q2063)

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DLMF:4.23.E39
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    Statements

    DLMF defining formula
    gd ⁡ ( x ) = ∫ 0 x sech ⁡ t ⁢ d t , Gudermannian 𝑥 superscript subscript 0 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\operatorname{gd}\left(x\right)=\int_{0}^{x}% \operatorname{sech}t\mathrm{d}t,}}
    0 references
    constraint
    - ∞ < x < ∞ 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    hyperbolic secant function
    DLMF defining formula
    sech ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    xml-id
    C4.S28.E6.m2adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1jdec
    0 references

    Identifiers

     
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