DLMF:11.7.E15 (Q4005)

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DLMF:11.7.E15
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ 𝐋 0 ⁡ ( t ) ⁢ d t = 2 π ⁢ a 2 - 1 ⁢ arcsin ⁡ ( 1 a ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 modified-Struve-L 0 𝑡 𝑡 2 𝜋 superscript 𝑎 2 1 1 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{L}_{0}\left(t% \right)\mathrm{d}t=\frac{2}{\pi\sqrt{a^{2}\!-\!1}}\operatorname{arcsin}\left(% \frac{1}{a}\right),}}
    0 references
    DLMF id
    DLMF:11.7.E15
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1amdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3amdec
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    Q11242
    Defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
    modified Struve function
    Defining formula
    𝐋 ν ⁡ ( z ) modified-Struve-L 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E2.m2abdec
    0 references
    Q11501
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C11.S7.XMD1.m1bdec
    0 references
     
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