SpecialFuncs.Besy Method

Overload List

#	Signature	Description
1	TCplx Besy(Double NU, TCplx Z)	Bessel function of the second kind, complex argument: Y_(nu)(z).
2	void Besy(Double NU, TCplx Z, TVec resCY, Boolean Scale)
3	TCplx Besy(Double NU, TCplx Z, Boolean Scale)	Bessel function of the second kind, complex argument, optional scaling: Y_(nu)(z).
4	TCplx Besy(Double NU, Double A)	Bessel function of the second kind, real argument: Y_(nu)(x).
5	TCplx Besy(Double NU, Double A, Boolean Scale)	Bessel function of the second kind, real argument, optional scaling: Y_(nu)(x).
6	TSCplx Besy(Single NU, TSCplx Z)
7	TSCplx Besy(Single NU, TSCplx Z, Boolean Scale)
8	TSCplx Besy(Single NU, Single A)
9	TSCplx Besy(Single NU, Single A, Boolean Scale)

Overload 1: TCplx Besy(Double NU, TCplx Z)

Bessel function of the second kind, complex argument: Y_(nu)(z).

#	Name	Description
1	Z	Defines complex value for which JYn(Z) should be evaluated.
2	NU	Defines the order of the Bessel function of the second kind Jn.

Returns: TCplx (complex) - Y_(nu)(z), the Bessel function of the second kind (Weber/Neumann function) of order NU, evaluated at the complex argument Z.

Remarks:

Y_(nu) is the second, singular-at-the-origin solution of Bessel's equation: Y_(nu)(z) = (J_(nu)(z)cos(nupi) - J_(-nu)(z))/sin(nupi) (the limit is taken for integer nu). Domain. Any finite complex Z, z != 0; order NU any real value.

Overload 2: void Besy(Double NU, TCplx Z, TVec resCY, Boolean Scale)

#	Name	Type	Description
1	NU	Double	scalar
2	Z	TCplx	scalar
3	resCY	TVec	source TVec
4	Scale	Boolean

Result: stored in self (calling object)

Overload 3: TCplx Besy(Double NU, TCplx Z, Boolean Scale)

Bessel function of the second kind, complex argument, optional scaling: Y_(nu)(z).

#	Name	Description
1	Z	Defines complex value for which Yn(Z) should be evaluated.
2	NU	Defines the order of the Bessel function of the second kind Yn.
3	Scale	If Scale parameter is true, Yn(Z) is multiplied by e^(-\|Im z\|).

Returns: TCplx (complex) - Y_(nu)(z) of order NU. When is true the result is multiplied by e^(-|Im z|), i.e. e^(-|Im z|) Y_(nu)(z).

Remarks:

Y_(nu)(z) = (J_(nu)(z)cos(nupi) - J_(-nu)(z))/sin(nupi) Domain. Any finite complex Z, z != 0; order NU any real value.

Overload 4: TCplx Besy(Double NU, Double A)

Bessel function of the second kind, real argument: Y_(nu)(x).

#	Name	Description
1	A	Defines real value for which JYn(Z) should be evaluated.
2	NU	Defines the order of the Bessel function of the second kind Jn.

Returns: TCplx (complex) - Y_(nu)(x) of order NU at the real argument A, returned as a TCplx (imaginary part zero for x>0).

Remarks:

Y_(nu)(z) = (J_(nu)(z)cos(nupi) - J_(-nu)(z))/sin(nupi) Domain. A>0 (real); Y_(nu) has a singularity at x=0 and is complex for x<0.

Overload 5: TCplx Besy(Double NU, Double A, Boolean Scale)

Bessel function of the second kind, real argument, optional scaling: Y_(nu)(x).

#	Name	Description
1	A	Defines real value for which Yn(A) should be evaluated.
2	NU	Defines the order of the Bessel function of the second kind Yn.
3	Scale	If Scale parameter is true, Yn(A) is multiplied by e^(-\|Im x\|).

Returns: TCplx (complex) - Y_(nu)(x) of order NU; when is true it is multiplied by e^(-|Im x|) (equal to 1 for real x).

Remarks:

Domain. A>0 (real).

Overload 6: TSCplx Besy(Single NU, TSCplx Z)

#	Name	Type	Description
1	NU	Single	scalar
2	Z	TSCplx	scalar

Returns: TSCplx

Overload 7: TSCplx Besy(Single NU, TSCplx Z, Boolean Scale)

#	Name	Type	Description
1	NU	Single	scalar
2	Z	TSCplx	scalar
3	Scale	Boolean

Returns: TSCplx

Overload 8: TSCplx Besy(Single NU, Single A)

#	Name	Type	Description
1	NU	Single	scalar
2	A	Single	scalar

Returns: TSCplx

Overload 9: TSCplx Besy(Single NU, Single A, Boolean Scale)

#	Name	Type	Description
1	NU	Single	scalar
2	A	Single	scalar
3	Scale	Boolean

Returns: TSCplx