SphericalBesselY
SphericalBesselY[n,z]
gives the spherical Bessel function of the second kind .
Details

- 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.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (32)
Numerical Evaluation (4)
Specific Values (4)
SphericalBesselY for symbolic n:
Find the first positive zero of SphericalBesselY:
Different SphericalBesselY types give different symbolic forms:
Visualization (3)
Plot the SphericalBesselY function for integer () and half-integer (
) orders:
Function Properties (7)
is defined for all real values greater than 0:
Complex domain is the whole plane except :
Approximate function range of :
Approximate function range of :
SphericalBesselY threads elementwise over lists:
TraditionalForm formatting:
Differentiation (3)
Integration (3)
Series Expansions (6)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
General term in the series expansion using SeriesCoefficient:
Find the series expansion at Infinity:
Function Identities and Simplifications (2)
Text
Wolfram Research (2007), SphericalBesselY, Wolfram Language function, https://reference.wolfram.com/language/ref/SphericalBesselY.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2007. "SphericalBesselY." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SphericalBesselY.html.
APA
Wolfram Language. (2007). SphericalBesselY. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SphericalBesselY.html