DLMF:15.8.E27 (Q5084): Difference between revisions

From DRMF
Jump to navigation Jump to search
Newer edit →
‎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|\operatorname{ph}z|<\pi}}

|\phase@@{z}|<\pi
Property / constraint: | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}} / rank
 
Normal rank

Revision as of 17:56, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:15.8.E27
No description defined

    Statements

    Defining formula
    2 ⁢ Γ ⁡ ( 1 2 ) ⁢ Γ ⁡ ( a + b + 1 2 ) Γ ⁡ ( a + 1 2 ) ⁢ Γ ⁡ ( b + 1 2 ) ⁢ F ⁡ ( a , b ; 1 2 ; z ) = F ⁡ ( 2 ⁢ a , 2 ⁢ b ; a + b + 1 2 ; 1 2 - 1 2 ⁢ z ) + F ⁡ ( 2 ⁢ a , 2 ⁢ b ; a + b + 1 2 ; 1 2 + 1 2 ⁢ z ) , 2 Euler-Gamma 1 2 Euler-Gamma 𝑎 𝑏 1 2 Euler-Gamma 𝑎 1 2 Euler-Gamma 𝑏 1 2 Gauss-hypergeometric-F 𝑎 𝑏 1 2 𝑧 Gauss-hypergeometric-F 2 𝑎 2 𝑏 𝑎 𝑏 1 2 1 2 1 2 𝑧 Gauss-hypergeometric-F 2 𝑎 2 𝑏 𝑎 𝑏 1 2 1 2 1 2 𝑧 {\displaystyle{\displaystyle\frac{2\Gamma\left(\tfrac{1}{2}\right)\Gamma\left(% a+b+\tfrac{1}{2}\right)}{\Gamma\left(a+\tfrac{1}{2}\right)\Gamma\left(b+\tfrac% {1}{2}\right)}F\left(a,b;\tfrac{1}{2};z\right)=F\left(2a,2b;a+b+\tfrac{1}{2};% \tfrac{1}{2}-\tfrac{1}{2}\sqrt{z}\right)+F\left(2a,2b;a+b+\tfrac{1}{2};\tfrac{% 1}{2}+\tfrac{1}{2}\sqrt{z}\right),}}
    0 references
    DLMF id
    DLMF:15.8.E27
    0 references
    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5084&oldid=19027"