SpecialFuncs.Besy Method

Overload List

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

Overload 1: function Besy(NU: Double; Z: TCplx): TCplx;

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

#NameDescription
1ZDefines complex value for which JYn(Z) should be evaluated.
2NUDefines 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: procedure Besy(NU: Double; Z: TCplx; resCY: TVec; Scale: Boolean);

#NameTypeDescription
1NUDoublescalar
2ZTCplxscalar
3resCYTVecsource TVec
4ScaleBoolean

Result: stored in self (calling object)

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

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

#NameDescription
1ZDefines complex value for which Yn(Z) should be evaluated.
2NUDefines the order of the Bessel function of the second kind Yn.
3ScaleIf 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.

See Also: SpecialFuncs.Airy, SpecialFuncs.Biry, SpecialFuncs.Besh, SpecialFuncs.Besk, SpecialFuncs.Besj, SpecialFuncs.EllipComplete, SpecialFuncs.EllipJacoby

Overload 4: function Besy(NU: Double; A: Double): TCplx;

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

#NameDescription
1ADefines real value for which JYn(Z) should be evaluated.
2NUDefines 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: function Besy(NU: Double; A: Double; Scale: Boolean): TCplx;

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

#NameDescription
1ADefines real value for which Yn(A) should be evaluated.
2NUDefines the order of the Bessel function of the second kind Yn.
3ScaleIf 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: function Besy(NU: Single; Z: TSCplx): TSCplx;

#NameTypeDescription
1NUSinglescalar
2ZTSCplxscalar

Returns: TSCplx

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

#NameTypeDescription
1NUSinglescalar
2ZTSCplxscalar
3ScaleBoolean

Returns: TSCplx

Overload 8: function Besy(NU: Single; A: Single): TSCplx;

#NameTypeDescription
1NUSinglescalar
2ASinglescalar

Returns: TSCplx

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

#NameTypeDescription
1NUSinglescalar
2ASinglescalar
3ScaleBoolean

Returns: TSCplx