gives the spherical Bessel function of the second kind .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- SphericalBesselY is given in terms of ordinary Bessel functions by .
- SphericalBesselY[n,z] has a branch cut discontinuity in the complex plane running from to .
- Explicit symbolic forms for integer n can be obtained using FunctionExpand.
- For certain special arguments, SphericalBesselY automatically evaluates to exact values.
- SphericalBesselY can be evaluated to arbitrary numerical precision.
- SphericalBesselY automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (4)
Plot the SphericalBesselY function for integer () and half-integer () orders:
Function Properties (7)
SphericalBesselY threads elementwise over lists:
Compute the indefinite integral using Integrate:
Series Expansions (6)
Find the Taylor expansion using Series:
General term in the series expansion using SeriesCoefficient:
Find the series expansion at Infinity:
Function Identities and Simplifications (2)
Use FullSimplify to simplify spherical Bessel functions of the second kind: