DLMF:10.49.E4 (Q3696)

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DLMF:10.49.E4
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    Statements

    test
    𝗒 n ⁡ ( z ) = - cos ⁡ ( z - 1 2 ⁢ n ⁢ π ) ⁢ ∑ k = 0 ⌊ n / 2 ⌋ ( - 1 ) k ⁢ a 2 ⁢ k ⁢ ( n + 1 2 ) z 2 ⁢ k + 1 + sin ⁡ ( z - 1 2 ⁢ n ⁢ π ) ⁢ ∑ k = 0 ⌊ ( n - 1 ) / 2 ⌋ ( - 1 ) k ⁢ a 2 ⁢ k + 1 ⁢ ( n + 1 2 ) z 2 ⁢ k + 2 . spherical-Bessel-Y 𝑛 𝑧 𝑧 1 2 𝑛 𝜋 superscript subscript 𝑘 0 𝑛 2 superscript 1 𝑘 subscript 𝑎 2 𝑘 𝑛 1 2 superscript 𝑧 2 𝑘 1 𝑧 1 2 𝑛 𝜋 superscript subscript 𝑘 0 𝑛 1 2 superscript 1 𝑘 subscript 𝑎 2 𝑘 1 𝑛 1 2 superscript 𝑧 2 𝑘 2 {\displaystyle{\displaystyle\mathsf{y}_{n}\left(z\right)=-\cos\left(z-\tfrac{1% }{2}n\pi\right)\sum_{k=0}^{\left\lfloor n/2\right\rfloor}(-1)^{k}\frac{a_{2k}(% n+\tfrac{1}{2})}{z^{2k+1}}+\sin\left(z-\tfrac{1}{2}n\pi\right)\sum_{k=0}^{% \left\lfloor(n-1)/2\right\rfloor}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k% +2}}.}}
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    DLMF id
    DLMF:10.49.E4
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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