DLMF:10.49.E2 (Q3692): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
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Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec

Revision as of 14:10, 2 January 2020

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DLMF:10.49.E2
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    𝗃 n ( z ) = sin ( z - 1 2 n π ) k = 0 n / 2 ( - 1 ) k a 2 k ( n + 1 2 ) z 2 k + 1 + cos ( 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-J 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{j}_{n}\left(z\right)=\sin\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}}+\cos\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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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references