DLMF:11.2.E7 (Q3922)

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DLMF:11.2.E7
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    Statements

    Defining formula
    d 2 w d z 2 + 1 z ⁢ d w d z + ( 1 - ν 2 z 2 ) ⁢ w = ( 1 2 ⁢ z ) ν - 1 π ⁢ Γ ⁡ ( ν + 1 2 ) . derivative 𝑤 𝑧 2 1 𝑧 derivative 𝑤 𝑧 1 superscript 𝜈 2 superscript 𝑧 2 𝑤 superscript 1 2 𝑧 𝜈 1 𝜋 Euler-Gamma 𝜈 1 2 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\frac{% 1}{z}\frac{\mathrm{d}w}{\mathrm{d}z}+\left(1-\frac{\nu^{2}}{z^{2}}\right)w=% \frac{(\tfrac{1}{2}z)^{\nu-1}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}.}}
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    DLMF id
    DLMF:11.2.E7
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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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.m2acdec
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