DLMF:15.5.E2 (Q5019)

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DLMF:15.5.E2
No description defined

    Statements

    Defining formula
    d n d z n ⁡ F ⁡ ( a , b ; c ; z ) = ( a ) n ⁢ ( b ) n ( c ) n ⁢ F ⁡ ( a + n , b + n ; c + n ; z ) . derivative 𝑧 𝑛 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 Pochhammer 𝑎 𝑛 Pochhammer 𝑏 𝑛 Pochhammer 𝑐 𝑛 Gauss-hypergeometric-F 𝑎 𝑛 𝑏 𝑛 𝑐 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}F\left(a% ,b;c;z\right)=\frac{{\left(a\right)_{n}}{\left(b\right)_{n}}}{{\left(c\right)_% {n}}}\*F\left(a+n,b+n;c+n;z\right).}}
    0 references
    DLMF id
    DLMF:15.5.E2
    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.m2aadec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    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.m2aadec
    0 references
    Q11650
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C15.S1.XMD10.m1dec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1adec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1adec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1adec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1adec
    0 references
     
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