DLMF:10.68.E9 (Q3875)

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DLMF:10.68.E9
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    bei ν x = 1 2 M ν + 1 sin ( θ ν + 1 - 1 4 π ) - 1 2 M ν - 1 sin ( θ ν - 1 - 1 4 π ) = ( ν / x ) M ν sin θ ν + M ν + 1 sin ( θ ν + 1 - 1 4 π ) = - ( ν / x ) M ν sin θ ν - M ν - 1 sin ( θ ν - 1 - 1 4 π ) . diffop Kelvin-bei 𝜈 1 𝑥 1 2 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 1 2 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 𝜈 𝑥 modulus-Bessel-M 𝜈 phase-Bessel-Theta 𝜈 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 𝜈 𝑥 modulus-Bessel-M 𝜈 phase-Bessel-Theta 𝜈 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 {\displaystyle{\displaystyle\operatorname{bei}_{\nu}'x=\tfrac{1}{2}M_{\nu+1}% \sin\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)-\tfrac{1}{2}M_{\nu-1}\sin\left% (\theta_{\nu-1}-\tfrac{1}{4}\pi\right)=(\nu/x)M_{\nu}\sin\theta_{\nu}+M_{\nu+1% }\sin\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)=-(\nu/x)M_{\nu}\sin\theta_{% \nu}-M_{\nu-1}\sin\left(\theta_{\nu-1}-\tfrac{1}{4}\pi\right).}}
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    DLMF:10.68.E9
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    bei ν ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C10.S61.E1.m3addec
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