DLMF:15.8.E12 (Q5069)

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DLMF:15.8.E12
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    Statements

    test
    𝐅 ⁑ ( a , b ; a + b - m ; z ) = ( 1 - z ) - m ⁒ 𝐅 ⁑ ( a ~ , b ~ ; a ~ + b ~ + m ; z ) , scaled-hypergeometric-bold-F π‘Ž 𝑏 π‘Ž 𝑏 π‘š 𝑧 superscript 1 𝑧 π‘š scaled-hypergeometric-bold-F ~ π‘Ž ~ 𝑏 ~ π‘Ž ~ 𝑏 π‘š 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;a+b-m;z\right)=(1-z)^{-m}% \mathbf{F}\left(\tilde{a},\tilde{b};\tilde{a}+\tilde{b}+m;z\right),}}
    0 references
    DLMF id
    DLMF:15.8.E12
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    constraint
    a ~ = a - m , b ~ = b - m formulae-sequence ~ π‘Ž π‘Ž π‘š ~ 𝑏 𝑏 π‘š {\displaystyle{\displaystyle\tilde{a}=a-m,\tilde{b}=b-m}}
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    Symbols used
    $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
    test
    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.m2aidec
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    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1kdec
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    Q11645
    test
    a π‘Ž {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1idec
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    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1idec
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    Q11651
    test
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C15.S1.XMD9.m1fdec
    0 references
     
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