DLMF:4.40.E15 (Q1987): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic secant function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
Defining formula:

arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}

\asech@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
xml-id: C4.S37.E8.m2adec

Revision as of 19:23, 1 January 2020

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DLMF:4.40.E15
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    Statements

    Defining formula
    ∫ arcsech ⁡ x ⁢ d x = x ⁢ arcsech ⁡ x + arcsin ⁡ x , hyperbolic-inverse-secant 𝑥 𝑥 𝑥 hyperbolic-inverse-secant 𝑥 𝑥 {\displaystyle{\displaystyle\int\operatorname{arcsech}x\mathrm{d}x=x% \operatorname{arcsech}x+\operatorname{arcsin}x,}}
    0 references
    DLMF id
    DLMF:4.40.E15
    0 references
    constraint
    0 < x < 1 0 𝑥 1 {\displaystyle{\displaystyle 0<x<1}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    inverse hyperbolic secant function
    Defining formula
    arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    xml-id
    C4.S37.E8.m2adec
    0 references
     
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