DLMF:15.4.E27 (Q5011)

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DLMF:15.4.E27
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    Statements

    Defining formula
    F ⁡ ( 1 , a ; a + 1 ; - 1 ) = 1 2 ⁢ a ⁢ ( ψ ⁡ ( 1 2 ⁢ a + 1 2 ) - ψ ⁡ ( 1 2 ⁢ a ) ) . Gauss-hypergeometric-F 1 𝑎 𝑎 1 1 1 2 𝑎 digamma 1 2 𝑎 1 2 digamma 1 2 𝑎 {\displaystyle{\displaystyle F\left(1,a;a+1;-1\right)=\tfrac{1}{2}a\left(\psi% \left(\tfrac{1}{2}a+\tfrac{1}{2}\right)-\psi\left(\tfrac{1}{2}a\right)\right).}}
    0 references
    DLMF id
    DLMF:15.4.E27
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aydec
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    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1tdec
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