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2.5.E45 - MaRDI portal

2.5.E45 (Q791)

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2.5.E45
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    Statements

    DLMF defining formula
    ℒ ⁡ h ⁡ ( ζ ) = ∫ 0 ∞ e - ζ ⁢ t 1 + t ⁢ d t , Laplace-transform ℎ 𝜁 superscript subscript 0 superscript 𝑒 𝜁 𝑡 1 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta% \right)=\int_{0}^{\infty}\frac{e^{-\zeta t}}{1+t}\mathrm{d}t,}}
    0 references
    constraint
    ℜ ⁡ ζ > 0 𝜁 0 {\displaystyle{\displaystyle\Re\zeta>0}}
    0 references
    Symbols used
    Laplace transform
    DLMF defining formula
    ℒ ⁡ ( f ) ⁡ ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E17.m2addec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1ahdec
    0 references
    locally integrable function
    DLMF defining formula
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD16.m1qdec
    0 references

    Identifiers

     
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