DLMF:4.38.E18 (Q1968)

From DRMF
Revision as of 13:07, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:4.38.E18
No description defined

    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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1968&oldid=7968"