DLMF:8.17.E16 (Q2657)

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DLMF:8.17.E16
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    Statements

    Defining formula
    a ⁢ I x ⁡ ( a + 1 , b ) = ( a + c ⁢ x ) ⁢ I x ⁡ ( a , b ) - c ⁢ x ⁢ I x ⁡ ( a - 1 , b ) , 𝑎 IncI 𝑥 𝑎 1 𝑏 𝑎 𝑐 𝑥 IncI 𝑥 𝑎 𝑏 𝑐 𝑥 IncI 𝑥 𝑎 1 𝑏 {\displaystyle{\displaystyle aI_{x}\left(a+1,b\right)=(a+cx)I_{x}\left(a,b% \right)-cxI_{x}\left(a-1,b\right),}}
    0 references
    DLMF id
    DLMF:8.17.E16
    0 references
    Symbols used
    incomplete beta function
    Defining formula
    I x ⁡ ( a , b ) IncI 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C8.S17.E2.m2aidec
    0 references
    Q11360
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1mdec
    0 references
    Q11361
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1ldec
    0 references
    Q11362
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1mdec
    0 references
     
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