DLMF:15.2.E2 (Q4978)

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DLMF:15.2.E2
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    Statements

    Defining formula
    𝐅 ⁑ ( a , b ; c ; z ) = βˆ‘ s = 0 ∞ ( a ) s ⁒ ( b ) s Ξ“ ⁑ ( c + s ) ⁒ s ! ⁒ z s , scaled-hypergeometric-bold-F π‘Ž 𝑏 𝑐 𝑧 superscript subscript 𝑠 0 Pochhammer π‘Ž 𝑠 Pochhammer 𝑏 𝑠 Euler-Gamma 𝑐 𝑠 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}{\left(b\right)_{s}}}{\Gamma\left(c+s\right)s!}z^{s}% ,}}
    0 references
    DLMF id
    DLMF:15.2.E2
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    Symbols used
    gamma function
    Defining formula
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
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