DLMF:4.21.E42 (Q1746): 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.m1xdec

Latest revision as of 18:29, 1 January 2020

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DLMF:4.21.E42
No description defined

    Statements

    Defining formula
    | cos ⁡ z | = ( cos 2 ⁡ x + sinh 2 ⁡ y ) 1 / 2 = ( 1 2 ⁢ ( cosh ⁡ ( 2 ⁢ y ) + cos ⁡ ( 2 ⁢ x ) ) ) 1 / 2 , 𝑧 superscript 2 𝑥 2 𝑦 1 2 superscript 1 2 2 𝑦 2 𝑥 1 2 {\displaystyle{\displaystyle|\cos z|=({\cos^{2}}x+{\sinh^{2}}y)^{1/2}=\left(% \tfrac{1}{2}(\cosh\left(2y\right)+\cos\left(2x\right))\right)^{1/2},}}
    0 references
    DLMF id
    DLMF:4.21.E42
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aaddec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aedec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2aedec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1edec
    0 references
    Q11222
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1edec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1xdec
    0 references
     
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