DLMF:4.35.E40 (Q1914): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1wdec

Latest revision as of 19:13, 1 January 2020

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DLMF:4.35.E40
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    Statements

    Defining formula
    | tanh ⁡ z | = ( cosh ⁡ ( 2 ⁢ x ) - cos ⁡ ( 2 ⁢ y ) cosh ⁡ ( 2 ⁢ x ) + cos ⁡ ( 2 ⁢ y ) ) 1 / 2 . 𝑧 superscript 2 𝑥 2 𝑦 2 𝑥 2 𝑦 1 2 {\displaystyle{\displaystyle|\tanh z|=\left(\frac{\cosh\left(2x\right)-\cos% \left(2y\right)}{\cosh\left(2x\right)+\cos\left(2y\right)}\right)^{1/2}.}}
    0 references
    DLMF id
    DLMF:4.35.E40
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2afdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aacdec
    0 references
    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2ahdec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1fdec
    0 references
    Q11222
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1fdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1wdec
    0 references
     
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