DLMF:4.38.E19 (Q1969): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: general inverse hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: general inverse hyperbolic tangent function / qualifier
 
Defining formula:

Arctanh ⁡ z multivalued-hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctanh}\NVar{z}}}

\Atanh@@{\NVar{z}}
Property / Symbols used: general inverse hyperbolic tangent function / qualifier
 
xml-id: C4.S37.E3.m2aadec

Latest revision as of 19:20, 1 January 2020

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DLMF:4.38.E19
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    Statements

    Defining formula
    Arctanh ⁡ u ± Arccoth ⁡ v = Arctanh ⁡ ( u ⁢ v ± 1 v ± u ) = Arccoth ⁡ ( v ± u u ⁢ v ± 1 ) . plus-or-minus multivalued-hyperbolic-inverse-tangent 𝑢 multivalued-hyperbolic-inverse-cotangent 𝑣 multivalued-hyperbolic-inverse-tangent plus-or-minus 𝑢 𝑣 1 plus-or-minus 𝑣 𝑢 multivalued-hyperbolic-inverse-cotangent plus-or-minus 𝑣 𝑢 plus-or-minus 𝑢 𝑣 1 {\displaystyle{\displaystyle\operatorname{Arctanh}u\pm\operatorname{Arccoth}v=% \operatorname{Arctanh}\left(\frac{uv\pm 1}{v\pm u}\right)=\operatorname{% Arccoth}\left(\frac{v\pm u}{uv\pm 1}\right).}}
    0 references
    DLMF id
    DLMF:4.38.E19
    0 references
    Symbols used
    general inverse hyperbolic cotangent function
    Defining formula
    Arccoth ⁡ z multivalued-hyperbolic-inverse-cotangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arccoth}\NVar{z}}}
    xml-id
    C4.S37.E6.m2adec
    0 references
    general inverse hyperbolic tangent function
    Defining formula
    Arctanh ⁡ z multivalued-hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctanh}\NVar{z}}}
    xml-id
    C4.S37.E3.m2aadec
    0 references
     
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