DLMF:4.23.E39 (Q1791): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: Gudermannian function / rank
 
Normal rank
Property / constraint
 

- < x < 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}

-\infty<x<\infty
Property / constraint: - < x < 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
Property / Symbols used
 
Property / Symbols used: hyperbolic secant function / rank
 
Normal rank
Property / Symbols used: hyperbolic secant function / qualifier
 
test:

sech z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

\sech@@{\NVar{z}}
Property / Symbols used: hyperbolic secant function / qualifier
 
xml-id: C4.S28.E6.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1jdec

Latest revision as of 17:36, 1 January 2020

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DLMF:4.23.E39
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    Statements

    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
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    - < x < 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1acdec
    0 references
    sech z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    C4.S28.E6.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3acdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1jdec
    0 references