DLMF:11.7.E6 (Q3995)

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DLMF:11.7.E6
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    Statements

    test
    f ν + 1 ⁢ ( z ) = ( 2 ⁢ ν + 1 ) ⁢ f ν ⁢ ( z ) - z ν + 1 ⁢ 𝐇 ν ⁡ ( z ) + ( 1 2 ⁢ z 2 ) ν + 1 ( ν + 1 ) ⁢ π ⁢ Γ ⁡ ( ν + 3 2 ) , subscript 𝑓 𝜈 1 𝑧 2 𝜈 1 subscript 𝑓 𝜈 𝑧 superscript 𝑧 𝜈 1 Struve-H 𝜈 𝑧 superscript 1 2 superscript 𝑧 2 𝜈 1 𝜈 1 𝜋 Euler-Gamma 𝜈 3 2 {\displaystyle{\displaystyle f_{\nu+1}(z)=(2\nu+1)f_{\nu}(z)-z^{\nu+1}\mathbf{% H}_{\nu}\left(z\right)+\frac{(\tfrac{1}{2}z^{2})^{\nu+1}}{(\nu+1)\sqrt{\pi}% \Gamma\left(\nu+\tfrac{3}{2}\right)},}}
    0 references
    DLMF id
    DLMF:11.7.E6
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    constraint
    ℜ ⁡ ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    Struve function
    test
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
     
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