Evaluate numerically:

Evaluate to high precision:

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

Evaluate for complex arguments and parameters:

Evaluate BesselY efficiently at high precision:

BesselY threads elementwise over lists and matrices:

Value of BesselY for integers () orders at :

For half-integer indices, BesselY evaluates to elementary functions:

Limiting value at infinity:

The first three zeros of :

Find the first zero of using Solve:

Visualize the result:

Plot the BesselY function for integer orders ():

Plot the real and imaginary parts of the BesselY function for integer orders ():

Plot the real part of :

Plot the imaginary part of :

is defined for all real values greater than 0:

Complex domain:

Approximate function range of :

Approximate function range of :

is not an analytic function:

BesselY is neither non-decreasing nor non-increasing:

BesselY is not injective:

BesselY is not surjective:

BesselY is neither non-negative nor non-positive:

has both singularity and discontinuity for z≤0:

BesselY is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Formula for the derivative:

Indefinite integral of BesselY:

Integrate expressions involving BesselY:

Definite integral of BesselY over its real domain:

Taylor expansion for around :

Plot the first three approximations for around :

General term in the series expansion of BesselY:

Asymptotic approximation of BesselY:

Taylor expansion at a generic point:

BesselY can be applied to a power series:

Compute the Laplace transform using LaplaceTransform:

HankelTransform:

MellinTransform:

Use FullSimplify to simplify Bessel functions:

Recurrence relation :

For integer and arbitrary fixed , :

Integral representation of BesselY:

Represent using BesselJ and Sin for non-integer :

BesselY can be represented in terms of MeijerG:

BesselY can be represented as a DifferenceRoot: