DLMF:15.9.E21 (Q5111)

From testwiki
Revision as of 13:11, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:15.9.E21
No description defined

    Statements

    test
    𝐅 ⁡ ( a , 1 - a c ; z ) = ( - z 1 - z ) ( 1 - c ) / 2 ⁢ P - a 1 - c ⁡ ( 1 - 2 ⁢ z ) , scaled-hypergeometric-bold-F 𝑎 1 𝑎 𝑐 𝑧 superscript 𝑧 1 𝑧 1 𝑐 2 Legendre-P-first-kind 1 𝑐 𝑎 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,1-a\atop c};z\right)=\left(% \frac{-z}{1-z}\right)^{\ifrac{(1-c)}{2}}\*P^{1-c}_{-a}\left(1-2z\right),}}
    0 references
    DLMF id
    DLMF:15.9.E21
    0 references
    constraint
    | ph ⁡ ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}
    0 references
    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5111&oldid=29254"