DLMF:4.38.E18 (Q1968): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: general inverse hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: general inverse hyperbolic sine function / qualifier
 
Defining formula:

Arcsinh ⁡ z multivalued-hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsinh}\NVar{z}}}

\Asinh@@{\NVar{z}}
Property / Symbols used: general inverse hyperbolic sine function / qualifier
 
xml-id: C4.S37.E1.m2aadec

Latest revision as of 19:20, 1 January 2020

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DLMF:4.38.E18
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    Statements

    Defining formula
    Arcsinh ⁡ u ± Arccosh ⁡ v = Arcsinh ⁡ ( u ⁢ v ± ( ( 1 + u 2 ) ⁢ ( v 2 - 1 ) ) 1 / 2 ) = Arccosh ⁡ ( v ⁢ ( 1 + u 2 ) 1 / 2 ± u ⁢ ( v 2 - 1 ) 1 / 2 ) , plus-or-minus multivalued-hyperbolic-inverse-sine 𝑢 multivalued-hyperbolic-inverse-cosine 𝑣 multivalued-hyperbolic-inverse-sine plus-or-minus 𝑢 𝑣 superscript 1 superscript 𝑢 2 superscript 𝑣 2 1 1 2 multivalued-hyperbolic-inverse-cosine plus-or-minus 𝑣 superscript 1 superscript 𝑢 2 1 2 𝑢 superscript superscript 𝑣 2 1 1 2 {\displaystyle{\displaystyle\operatorname{Arcsinh}u\pm\operatorname{Arccosh}v=% \operatorname{Arcsinh}\left(uv\pm((1+u^{2})(v^{2}-1))^{1/2}\right)=% \operatorname{Arccosh}\left(v(1+u^{2})^{1/2}\pm u(v^{2}-1)^{1/2}\right),}}
    0 references
    DLMF id
    DLMF:4.38.E18
    0 references
    Symbols used
    general inverse hyperbolic cosine function
    Defining formula
    Arccosh ⁡ z multivalued-hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccosh}\NVar{z}}}
    xml-id
    C4.S37.E2.m2aadec
    0 references
    general inverse hyperbolic sine function
    Defining formula
    Arcsinh ⁡ z multivalued-hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsinh}\NVar{z}}}
    xml-id
    C4.S37.E1.m2aadec
    0 references
     
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