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DLMF:12.14.E22 - MaRDI portal

DLMF:12.14.E22 (Q4959)

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DLMF:12.14.E22
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    Statements

    DLMF defining formula
    c 2 ⁢ r + i ⁢ d 2 ⁢ r = Γ ⁡ ( 2 ⁢ r + 1 2 + i ⁢ a ) Γ ⁡ ( 1 2 + i ⁢ a ) . subscript 𝑐 2 𝑟 𝑖 subscript 𝑑 2 𝑟 Euler-Gamma 2 𝑟 1 2 𝑖 𝑎 Euler-Gamma 1 2 𝑖 𝑎 {\displaystyle{\displaystyle c_{2r}+id_{2r}=\frac{\Gamma\left(2r+\tfrac{1}{2}+% ia\right)}{\Gamma\left(\tfrac{1}{2}+ia\right)}.}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
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    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1rdec
    0 references
     
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