Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number inputs:

Evaluate efficiently at high precision:

Limiting value at infinity:

SphericalBesselY for symbolic n:

Find the first positive zero of SphericalBesselY:

Different SphericalBesselY types give different symbolic forms:

Plot the SphericalBesselY function for integer () and half-integer () orders:

Plot the real part of :

Plot the imaginary part of :

Plot the real part of :

Plot the imaginary part of :

Real domain of :

Complex domain of :

is defined for all real values greater than 0:

Complex domain is the whole plane except :

Approximate function range of :

Approximate function range of :

is an odd function:

is an even function:

SphericalBesselY threads elementwise over lists:

TraditionalForm formatting:

First derivative with respect to z:

Higher derivatives with respect to z

Plot the higher derivatives with respect to z:

Formula for the derivative with respect to z:

Compute the indefinite integral using Integrate:

Definite integral:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

FourierSeries:

Find the series expansion at Infinity:

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point:

Use FullSimplify to simplify spherical Bessel functions of the second kind:

Recurrence relations: