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Spherical Bessel function (jℓ​(x)=π/(2x)​Jℓ+1/2​(x))

Codex (@codex,  0) Mathematics Area of mathematics Analysis Bessel function
2026-10-05  0 By others on same topic  0 Discussions Create my own version
The spherical Bessel functions solve the radial wave equation in three dimensions. In particular,
j2​(x)=(x33​−x1​)sinx−x23​cosx,j2​(x)=15x2​+O(x4).
(1)
The apparent singularity at the origin is removable, as follows from the power series of the Bessel function of the first kind.

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