DLMF:15.5.E15 (Q5032): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1mdec

Revision as of 13:54, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:15.5.E15
No description defined

    Statements

    Defining formula
    ( c - a - 1 ) ⁢ F ⁡ ( a , b ; c ; z ) + a ⁢ F ⁡ ( a + 1 , b ; c ; z ) - ( c - 1 ) ⁢ F ⁡ ( a , b ; c - 1 ; z ) = 0 , 𝑐 𝑎 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle(c-a-1)F\left(a,b;c;z\right)+aF\left(a+1,b;c;z% \right)-(c-1)F\left(a,b;c-1;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E15
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2amdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1ndec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1mdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5032&oldid=41432"