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DLMF:8.21.E22 - MaRDI portal

DLMF:8.21.E22 (Q3442)

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DLMF:8.21.E22
No description defined

    Statements

    DLMF defining formula
    f ⁢ ( a , z ) = ∫ 0 ∞ sin ⁡ t ( t + z ) 1 - a ⁢ d t , 𝑓 𝑎 𝑧 superscript subscript 0 𝑡 superscript 𝑡 𝑧 1 𝑎 𝑡 {\displaystyle{\displaystyle f(a,z)=\int_{0}^{\infty}\frac{\sin t}{(t+z)^{1-a}% }\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.m1aedec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2ahdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1rdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1sdec
    0 references
    auxiliary function (locally)
    DLMF defining formula
    f ⁢ ( a , z ) 𝑓 𝑎 𝑧 {\displaystyle{\displaystyle f(a,z)}}
    xml-id
    C8.S21.XMD1.m1cdec
    0 references

    Identifiers

     
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