DLMF:10.18.E16 (Q3209)

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DLMF:10.18.E16
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    θ ν 2 ( x ) + 1 2 θ ν ′′′ ( x ) θ ν ( x ) - 3 4 ( θ ν ′′ ( x ) θ ν ( x ) ) 2 = 1 - ν 2 - 1 4 x 2 . diffop phase-Bessel-Theta 𝜈 1 2 𝑥 1 2 diffop phase-Bessel-Theta 𝜈 3 𝑥 diffop phase-Bessel-Theta 𝜈 1 𝑥 3 4 superscript diffop phase-Bessel-Theta 𝜈 2 𝑥 diffop phase-Bessel-Theta 𝜈 1 𝑥 2 1 superscript 𝜈 2 1 4 superscript 𝑥 2 {\displaystyle{\displaystyle{\theta_{\nu}'^{2}}\left(x\right)+\frac{1}{2}\frac% {\theta_{\nu}'''\left(x\right)}{\theta_{\nu}'\left(x\right)}-\frac{3}{4}\left(% \frac{\theta_{\nu}''\left(x\right)}{\theta_{\nu}'\left(x\right)}\right)^{2}=1-% \frac{\nu^{2}-\tfrac{1}{4}}{x^{2}}.}}
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    DLMF:10.18.E16
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