DLMF:2.8.E17 (Q951)

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DLMF:2.8.E17
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    B s ( ξ ) = { 1 2 ξ 1 / 2 0 ξ ( ψ ( v ) A s ( v ) - A s ′′ ( v ) ) d v v 1 / 2 , ξ > 0 , 1 2 ( - ξ ) 1 / 2 ξ 0 ( ψ ( v ) A s ( v ) - A s ′′ ( v ) ) d v ( - v ) 1 / 2 , ξ < 0 , subscript 𝐵 𝑠 𝜉 cases 1 2 superscript 𝜉 1 2 superscript subscript 0 𝜉 𝜓 𝑣 subscript 𝐴 𝑠 𝑣 superscript subscript 𝐴 𝑠 ′′ 𝑣 𝑣 superscript 𝑣 1 2 𝜉 0 1 2 superscript 𝜉 1 2 superscript subscript 𝜉 0 𝜓 𝑣 subscript 𝐴 𝑠 𝑣 superscript subscript 𝐴 𝑠 ′′ 𝑣 𝑣 superscript 𝑣 1 2 𝜉 0 {\displaystyle{\displaystyle B_{s}(\xi)=\begin{cases}\dfrac{1}{2\xi^{1/2}}% \displaystyle\int_{0}^{\xi}\left(\psi(v)A_{s}(v)-A_{s}^{\prime\prime}(v)\right% )\dfrac{\mathrm{d}v}{v^{1/2}},&\xi>0,\\ \dfrac{1}{2(-\xi)^{1/2}}\displaystyle\int_{\xi}^{0}\left(\psi(v)A_{s}(v)-A_{s}% ^{\prime\prime}(v)\right)\dfrac{\mathrm{d}v}{(-v)^{1/2}},&\xi<0,\end{cases}}}
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    DLMF:2.8.E17
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