DLMF:4.35.E26 (Q1900): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine function / qualifier
 
Defining formula:

cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

\cosh@@{\NVar{z}}
Property / Symbols used: hyperbolic cosine function / qualifier
 
xml-id: C4.S28.E2.m2aqdec
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.m2apdec
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.m2aedec
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.m1idec

Latest revision as of 19:11, 1 January 2020

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DLMF:4.35.E26
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    Statements

    sinh ( 2 z ) = 2 sinh z cosh z = 2 tanh z 1 - tanh 2 z , 2 𝑧 2 𝑧 𝑧 2 𝑧 1 2 𝑧 {\displaystyle{\displaystyle\sinh\left(2z\right)=2\sinh z\cosh z=\frac{2\tanh z% }{1-{\tanh^{2}}z},}}
    0 references
    DLMF:4.35.E26
    0 references
    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2aqdec
    0 references
    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2apdec
    0 references
    tanh z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    C4.S28.E4.m2aedec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1idec
    0 references