DLMF:15.5.E20 (Q5037)

From DRMF
Revision as of 13:55, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:15.5.E20
No description defined

    Statements

    Defining formula
    z ⁢ ( 1 - z ) ⁢ ( d F ⁡ ( a , b ; c ; z ) / d z ) = ( c - a ) ⁢ F ⁡ ( a - 1 , b ; c ; z ) + ( a - c + b ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) = ( c - b ) ⁢ F ⁡ ( a , b - 1 ; c ; z ) + ( b - c + a ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) , 𝑧 1 𝑧 derivative Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑧 𝑐 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑎 𝑐 𝑏 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑐 𝑏 Gauss-hypergeometric-F 𝑎 𝑏 1 𝑐 𝑧 𝑏 𝑐 𝑎 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle z(1-z)\left(\ifrac{\mathrm{d}F\left(a,b;c;z\right% )}{\mathrm{d}z}\right)=(c-a)F\left(a-1,b;c;z\right)+(a-c+bz)F\left(a,b;c;z% \right)=(c-b)F\left(a,b-1;c;z\right)+(b-c+az)F\left(a,b;c;z\right),}}
    0 references
    DLMF id
    DLMF:15.5.E20
    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.m2ardec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2ajdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1sdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1rdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1rdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1rdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5037&oldid=41612"