DLMF:4.35.E38 (Q1912): Difference between revisions

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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.m2azdec

Revision as of 19:13, 1 January 2020

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DLMF:4.35.E38
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    Statements

    Defining formula
    | sinh ⁡ z | = ( sinh 2 ⁡ x + sin 2 ⁡ y ) 1 / 2 = ( 1 2 ⁢ ( cosh ⁡ ( 2 ⁢ x ) - cos ⁡ ( 2 ⁢ y ) ) ) 1 / 2 , 𝑧 superscript 2 𝑥 2 𝑦 1 2 superscript 1 2 2 𝑥 2 𝑦 1 2 {\displaystyle{\displaystyle|\sinh z|=({\sinh^{2}}x+{\sin^{2}}y)^{1/2}=\left(% \tfrac{1}{2}(\cosh\left(2x\right)-\cos\left(2y\right))\right)^{1/2},}}
    0 references
    DLMF id
    DLMF:4.35.E38
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aaadec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2azdec
    0 references
     
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