DLMF:4.32.E4 (Q1857): 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: hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic tangent function / qualifier
 
Defining formula:

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

\tanh@@{\NVar{z}}
Property / Symbols used: hyperbolic tangent function / qualifier
 
xml-id: C4.S28.E4.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
Defining formula:

arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7adec
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.m1cdec

Latest revision as of 19:06, 1 January 2020

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DLMF:4.32.E4
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    Statements

    arctan x 1 2 π tanh x , 𝑥 1 2 𝜋 𝑥 {\displaystyle{\displaystyle\operatorname{arctan}x\leq\tfrac{1}{2}\pi\tanh x,}}
    0 references
    DLMF:4.32.E4
    0 references
    x 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    tanh z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    C4.S28.E4.m2aadec
    0 references
    arctan z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    C4.S23.SS2.p1.m7adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1cdec
    0 references