DLMF:14.5.E20 (Q4732)

From DRMF
Revision as of 01:24, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.5.E20
No description defined

    Statements

    Defining formula
    𝖯 1 2 ⁡ ( cos ⁡ θ ) = 2 π ⁢ ( 2 ⁢ E ⁡ ( sin ⁡ ( 1 2 ⁢ θ ) ) - K ⁡ ( sin ⁡ ( 1 2 ⁢ θ ) ) ) , shorthand-Ferrers-Legendre-P-first-kind 1 2 𝜃 2 𝜋 2 complete-elliptic-integral-second-kind-E 1 2 𝜃 complete-elliptic-integral-first-kind-K 1 2 𝜃 {\displaystyle{\displaystyle\mathsf{P}_{\frac{1}{2}}\left(\cos\theta\right)=% \frac{2}{\pi}\left(2E\left(\sin\left(\tfrac{1}{2}\theta\right)\right)-K\left(% \sin\left(\tfrac{1}{2}\theta\right)\right)\right),}}
    0 references
    DLMF id
    DLMF:14.5.E20
    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.m2akdec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4732&oldid=31139"