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DLMF:11.2.E9 - MaRDI portal

DLMF:11.2.E9 (Q4621)

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DLMF:11.2.E9
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    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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    Failed to parse (LaTeXML (experimental; uses MathML) timeout from "http://latexml:8080/convert/".): {\displaystyle \EulerGamma@{\NVar{z}}}
    C5.S2.E1.m2acdec
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    Failed to parse (LaTeXML (experimental; uses MathML) timeout from "http://latexml:8080/convert/".): {\displaystyle \cpi}
    C3.S12.E1.m2addec
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    Failed to parse (LaTeXML (experimental; uses MathML) timeout from "http://latexml:8080/convert/".): {\displaystyle \deriv{\NVar{f}}{\NVar{x}}}
    C1.S4.E4.m2aadec
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    Failed to parse (LaTeXML (experimental; uses MathML) timeout from "http://latexml:8080/convert/".): {\displaystyle z}
    C11.S1.XMD2.m1hdec
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    Failed to parse (LaTeXML (experimental; uses MathML) timeout from "http://latexml:8080/convert/".): {\displaystyle \nu}
    C11.S1.XMD3.m1fdec
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