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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    Q10759
    Defining formula
    ( a ) n Pochhammer π‘Ž 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    scaled (or Olver’s) generalized hypergeometric function
    Defining formula
    𝐅 q p ⁑ ( 𝐚 ; 𝐛 ; ) hypergeometric-bold-pFq 𝑝 π‘ž 𝐚 𝐛 {\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C16.S2.E5.m2adec
    0 references
    Q11648
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C15.S1.XMD11.m1adec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1adec
    0 references
     
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