DLMF:15.4.E24 (Q5008)

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DLMF:15.4.E24
No description defined

    Statements

    Defining formula
    F ⁡ ( - n , b ; c ; 1 ) = ( c - b ) n ( c ) n , Gauss-hypergeometric-F 𝑛 𝑏 𝑐 1 Pochhammer 𝑐 𝑏 𝑛 Pochhammer 𝑐 𝑛 {\displaystyle{\displaystyle F\left(-n,b;c;1\right)=\frac{{\left(c-b\right)_{n% }}}{{\left(c\right)_{n}}},}}
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    DLMF id
    DLMF:15.4.E24
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    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    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.m2awdec
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    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    Q11650
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C15.S1.XMD10.m1dec
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    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1fdec
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    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1cdec
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