DLMF:15.9.E18 (Q5108): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / constraint
 

| ph ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}

\abs{\phase@{-z}}<\pi
Property / constraint: | ph ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}} / rank
 
Normal rank

Revision as of 17:56, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:15.9.E18
No description defined

    Statements

    𝐅 ( a , b a + b + 1 2 ; z ) = 2 a + b - ( 1 / 2 ) ( - z ) ( - a - b + ( 1 / 2 ) ) / 2 P a - b - ( 1 / 2 ) - a - b + ( 1 / 2 ) ( 1 - z ) , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑎 𝑏 1 2 𝑧 superscript 2 𝑎 𝑏 1 2 superscript 𝑧 𝑎 𝑏 1 2 2 Legendre-P-first-kind 𝑎 𝑏 1 2 𝑎 𝑏 1 2 1 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop a+b+\tfrac{1}{2}};z% \right)=2^{a+b-(\ifrac{1}{2})}(-z)^{(-a-b+(\ifrac{1}{2}))/2}\*P^{-a-b+(\ifrac{% 1}{2})}_{a-b-(\ifrac{1}{2})}\left(\sqrt{1-z}\right),}}
    0 references
    DLMF:15.9.E18
    0 references
    | ph ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}
    0 references