DLMF:11.4.E8 (Q3940)

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DLMF:11.4.E8
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    Statements

    Defining formula
    𝐋 - 1 2 ⁡ ( z ) = ( 2 π ⁢ z ) 1 2 ⁢ sinh ⁡ z , modified-Struve-L 1 2 𝑧 superscript 2 𝜋 𝑧 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{-\frac{1}{2}}\left(z\right)=\left(% \frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh z,}}
    0 references
    DLMF id
    DLMF:11.4.E8
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
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    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.m2acdec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1gdec
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