DLMF:4.40.E6 (Q1978): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aedec
Property / Symbols used
 
Property / Symbols used: hyperbolic cotangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic cotangent function / qualifier
 
Defining formula:

coth z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}

\coth@@{\NVar{z}}
Property / Symbols used: hyperbolic cotangent function / qualifier
 
xml-id: C4.S28.E7.m2adec
Property / Symbols used
 
Property / Symbols used: hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: hyperbolic sine function / qualifier
 
Defining formula:

sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aedec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1edec

Latest revision as of 19:21, 1 January 2020

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DLMF:4.40.E6
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    Statements

    coth x d x = ln ( sinh x ) , hyperbolic-cotangent 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\int\coth x\mathrm{d}x=\ln\left(\sinh x\right),}}
    0 references
    DLMF:4.40.E6
    0 references
    0 < x < 0 𝑥 {\displaystyle{\displaystyle 0<x<\infty}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aedec
    0 references
    coth z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    C4.S28.E7.m2adec
    0 references
    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2abdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aedec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1edec
    0 references