DLMF:11.4.E30 (Q3962)

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DLMF:11.4.E30
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    Statements

    Defining formula
    d d z ⁡ ( z - ν ⁢ 𝐋 ν ⁡ ( z ) ) = 2 - ν π ⁢ Γ ⁡ ( ν + 3 2 ) + z - ν ⁢ 𝐋 ν + 1 ⁡ ( z ) . derivative 𝑧 superscript 𝑧 𝜈 modified-Struve-L 𝜈 𝑧 superscript 2 𝜈 𝜋 Euler-Gamma 𝜈 3 2 superscript 𝑧 𝜈 modified-Struve-L 𝜈 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\left(z^{-\nu}% \mathbf{L}_{\nu}\left(z\right)\right)=\frac{2^{-\nu}}{\sqrt{\pi}\Gamma\left(% \nu+\tfrac{3}{2}\right)}+z^{-\nu}\mathbf{L}_{\nu+1}\left(z\right).}}
    0 references
    DLMF id
    DLMF:11.4.E30
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
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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.m2avdec
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2acdec
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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.m2ajdec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1abdec
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