DLMF:11.4.E25 (Q3957)

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DLMF:11.4.E25
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    Statements

    Defining formula
    𝐋 ν - 1 ⁡ ( z ) - 𝐋 ν + 1 ⁡ ( z ) = 2 ⁢ ν z ⁢ 𝐋 ν ⁡ ( z ) + ( 1 2 ⁢ z ) ν π ⁢ Γ ⁡ ( ν + 3 2 ) , modified-Struve-L 𝜈 1 𝑧 modified-Struve-L 𝜈 1 𝑧 2 𝜈 𝑧 modified-Struve-L 𝜈 𝑧 superscript 1 2 𝑧 𝜈 𝜋 Euler-Gamma 𝜈 3 2 {\displaystyle{\displaystyle\mathbf{L}_{\nu-1}\left(z\right)-\mathbf{L}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{L}_{\nu}\left(z\right)+\frac{(\tfrac{1}{% 2}z)^{\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}\right)},}}
    0 references
    DLMF id
    DLMF:11.4.E25
    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.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2asdec
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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.m2agdec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1wdec
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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1jdec
    0 references
     
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