DLMF:33.14.E8 (Q9617): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec

Revision as of 14:32, 2 January 2020

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DLMF:33.14.E8
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    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
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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