DLMF:10.60.E10 (Q3785)

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DLMF:10.60.E10
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    test
    J 0 ⁡ ( z ⁢ sin ⁡ α ) = ∑ n = 0 ∞ ( 4 ⁢ n + 1 ) ⁢ ( 2 ⁢ n ) ! 2 2 ⁢ n ⁢ ( n ! ) 2 ⁢ 𝗃 2 ⁢ n ⁡ ( z ) ⁢ P 2 ⁢ n ⁡ ( cos ⁡ α ) . Bessel-J 0 𝑧 𝛼 superscript subscript 𝑛 0 4 𝑛 1 2 𝑛 superscript 2 2 𝑛 superscript 𝑛 2 spherical-Bessel-J 2 𝑛 𝑧 shorthand-Legendre-P-first-kind 2 𝑛 𝛼 {\displaystyle{\displaystyle J_{0}\left(z\sin\alpha\right)=\sum_{n=0}^{\infty}% (4n+1)\frac{(2n)!}{2^{2n}(n!)^{2}}\mathsf{j}_{2n}\left(z\right)P_{2n}\left(% \cos\alpha\right).}}
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    DLMF id
    DLMF:10.60.E10
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