DLMF:4.40.E10 (Q1982): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic tangent function / qualifier
 
test:

tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}

\tanh@@{\NVar{z}}
Property / Symbols used: hyperbolic tangent function / qualifier
 
xml-id: C4.S28.E4.m2abdec
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.m3aidec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11221 / rank
 
Normal rank
Property / Symbols used: Q11221 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11221 / qualifier
 
xml-id: C4.S1.XMD4.m1cdec
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.m1idec

Latest revision as of 18:22, 1 January 2020

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English
DLMF:4.40.E10
No description defined

    Statements

    test
    ∫ 0 ∞ tanh ⁡ ( a ⁢ x ) - tanh ⁡ ( b ⁢ x ) x ⁢ d x = ln ⁡ ( a b ) , superscript subscript 0 𝑎 𝑥 𝑏 𝑥 𝑥 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle{\int_{0}^{\infty}\frac{\tanh\left(ax\right)-\tanh% \left(bx\right)}{x}\mathrm{d}x=\ln\left(\frac{a}{b}\right)},}}
    0 references
    DLMF id
    DLMF:4.40.E10
    0 references
    constraint
    b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    hyperbolic tangent function
    test
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11221
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1cdec
    0 references
    Q11218
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1idec
    0 references
     
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