DLMF:11.7.E14 (Q4004)

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DLMF:11.7.E14
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ 𝐇 1 ⁡ ( t ) ⁢ d t = 2 π ⁢ a - 2 ⁢ a π ⁢ 1 + a 2 ⁢ ln ⁡ ( 1 + 1 + a 2 a ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 Struve-H 1 𝑡 𝑡 2 𝜋 𝑎 2 𝑎 𝜋 1 superscript 𝑎 2 1 1 superscript 𝑎 2 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{H}_{1}\left(t% \right)\mathrm{d}t=\frac{2}{\pi a}-\frac{2a}{\pi\sqrt{1+a^{2}}}\ln\left(\frac{% 1+\sqrt{1+a^{2}}}{a}\right),}}
    0 references
    DLMF id
    DLMF:11.7.E14
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    Symbols used
    Struve function
    Defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2akdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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