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DLMF:8.21.E24 - MaRDI portal

DLMF:8.21.E24 (Q3444)

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DLMF:8.21.E24
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    Statements

    f ( a , z ) = z a 2 0 ( ( 1 + i t ) a - 1 + ( 1 - i t ) a - 1 ) e - z t d t , 𝑓 𝑎 𝑧 superscript 𝑧 𝑎 2 superscript subscript 0 superscript 1 𝑖 𝑡 𝑎 1 superscript 1 𝑖 𝑡 𝑎 1 superscript 𝑒 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle f(a,z)=\frac{z^{a}}{2}\int_{0}^{\infty}\left((1+% it)^{a-1}+(1-it)^{a-1}\right)e^{-zt}\mathrm{d}t,}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1agdec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3agdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1tdec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1udec
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    f ( a , z ) 𝑓 𝑎 𝑧 {\displaystyle{\displaystyle f(a,z)}}
    C8.S21.XMD1.m1ddec
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    Identifiers