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BesselY

BesselY[n, z]
gives the Bessel function of the second kind Y_n(z).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Y_n(z) satisfies the differential equation z^2y^('')+zy^'+(z^2-n^2)y=0.
  • BesselY[n, z] has a branch cut discontinuity in the complex z plane running from -infty to 0.
  • For certain special arguments, BesselY automatically evaluates to exact values.
  • BesselY can be evaluated to arbitrary numerical precision.
  • BesselY automatically threads over lists.
EXAMPLESCLOSE ALL
Scope   (6)
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
BesselY threads element-wise over lists:
For half-integer indices, BesselY evaluates to elementary functions:
TraditionalForm formatting:
Generalizations & Extensions   (1)
BesselY can be applied to a power series:
Applications   (1)
Solve the Bessel differential equation:
Properties & Relations   (2)
Use FullSimplify to simplify Bessel functions:
Integrate expressions involving BesselY:
Possible Issues   (1)
With numeric arguments, half-integer Bessel functions are not automatically evaluated:
For symbolic arguments they are:
This can lead to major inaccuracies in machine-precision evaluation:
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