DLMF:33.14.E8 (Q9617)

From DRMF
Revision as of 16:29, 30 December 2019 by Admin (talk | contribs) (‎Changed an Item: Wikidata Toolkit example test statement addition)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:33.14.E8
No description defined

    Statements

    Defining formula
    S ⁢ ( ϵ , r ) = { 2 ⁢ cos ⁡ ( π ⁢ | ϵ | - 1 / 2 ) , ϵ < 0 , r > 0 , 0 , ϵ < 0 , r < 0 , e π ⁢ ϵ - 1 / 2 , ϵ > 0 , r > 0 , e - π ⁢ ϵ - 1 / 2 , ϵ > 0 , r < 0 . 𝑆 italic-ϵ 𝑟 cases 2 𝜋 superscript italic-ϵ 1 2 formulae-sequence italic-ϵ 0 𝑟 0 0 formulae-sequence italic-ϵ 0 𝑟 0 superscript 𝑒 𝜋 superscript italic-ϵ 1 2 formulae-sequence italic-ϵ 0 𝑟 0 superscript 𝑒 𝜋 superscript italic-ϵ 1 2 formulae-sequence italic-ϵ 0 𝑟 0 {\displaystyle{\displaystyle S(\epsilon,r)=\begin{cases}2\cos\left(\pi|% \epsilon|^{-1/2}\right),&\epsilon<0,r>0,\\ 0,&\epsilon<0,r<0,\\ e^{\pi\epsilon^{-1/2}},&\epsilon>0,r>0,\\ e^{-\pi\epsilon^{-1/2}},&\epsilon>0,r<0.\end{cases}}}
    0 references
    DLMF id
    DLMF:33.14.E8
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9617&oldid=17436"