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DLMF:4.40.E5 - MaRDI portal

DLMF:4.40.E5 (Q2435)

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DLMF:4.40.E5
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    Statements

    DLMF defining formula
    ∫ sech ⁡ x ⁢ d x = gd ⁡ ( x ) . 𝑥 𝑥 Gudermannian 𝑥 {\displaystyle{\displaystyle\int\operatorname{sech}x\mathrm{d}x=\operatorname{% gd}\left(x\right).}}
    0 references
    Symbols used
    Gudermannian function
    DLMF defining formula
    gd ⁡ x Gudermannian 𝑥 {\displaystyle{\displaystyle\operatorname{gd}\NVar{x}}}
    xml-id
    C4.S23.E39.m2adec
    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
    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.m3addec
    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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