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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

    DLMF defining formula
    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
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1tdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1udec
    0 references
    auxiliary function (locally)
    DLMF defining formula
    f ⁢ ( a , z ) 𝑓 𝑎 𝑧 {\displaystyle{\displaystyle f(a,z)}}
    xml-id
    C8.S21.XMD1.m1ddec
    0 references

    Identifiers

     
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