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DLMF:14.3.E3 - MaRDI portal

DLMF:14.3.E3 (Q5389)

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DLMF:14.3.E3
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    Statements

    DLMF defining formula
    𝐅 ⁑ ( a , b ; c ; x ) = 1 Ξ“ ⁑ ( c ) ⁒ F ⁑ ( a , b ; c ; x ) scaled-hypergeometric-bold-F π‘Ž 𝑏 𝑐 π‘₯ 1 Euler-Gamma 𝑐 Gauss-hypergeometric-F π‘Ž 𝑏 𝑐 π‘₯ {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;x\right)=\frac{1}{\Gamma% \left(c\right)}F\left(a,b;c;x\right)}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    DLMF defining formula
    F ⁑ ( a , b ; c ; z ) Gauss-hypergeometric-F π‘Ž 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2adec
    0 references
    Olver’s hypergeometric function
    DLMF defining formula
    𝐅 ⁑ ( a , b ; c ; z ) scaled-hypergeometric-bold-F π‘Ž 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}
    xml-id
    C15.S2.E2.m2abdec
    0 references
    real variable
    DLMF defining formula
    x π‘₯ {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1bdec
    0 references

    Identifiers

     
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