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DLMF:11.7.E13 - MaRDI portal

DLMF:11.7.E13 (Q4700)

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DLMF:11.7.E13
No description defined

    Statements

    DLMF defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ 𝐇 0 ⁡ ( t ) ⁢ d t = 2 π ⁢ 1 + a 2 ⁢ ln ⁡ ( 1 + 1 + a 2 a ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 Struve-H 0 𝑡 𝑡 2 𝜋 1 superscript 𝑎 2 1 1 superscript 𝑎 2 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathbf{H}_{0}\left(t% \right)\mathrm{d}t=\frac{2}{\pi\sqrt{1+a^{2}}}\ln\left(\frac{1+\sqrt{1+a^{2}}}% {a}\right),}}
    0 references
    Symbols used
    Struve function
    DLMF defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2ajdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C11.S7.XMD1.m1dec
    0 references

    Identifiers

     
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