DEFINITION MODULE SpezFunkt3;
(*------------------------------------------------------------------------*)
(* Stellt verschiedene mathematische Funktionen zur Verf"ugung *)
(* This library provides some special mathematical functions. *)
(*------------------------------------------------------------------------*)
(* Implementation : Michael Riedl *)
(* Licence : GNU Lesser General Public License (LGPL) *)
(*------------------------------------------------------------------------*)
(* $Id: SpezFunkt3.def,v 1.4 2018/05/16 07:08:32 mriedl Exp mriedl $ *)
PROCEDURE DBesselJ0(x : LONGREAL) : LONGREAL;
(*----------------------------------------------------------------*)
(* Berechnet die Bessel Function erster Art der Ordnung Null *)
(* fuer das Argument x. Abgeleitet aus der CERN library 2006. *)
(*----------------------------------------------------------------*)
PROCEDURE BesselJ0(x : LONGREAL) : LONGREAL;
(*----------------------------------------------------------------*)
(* Berechnet die Besselfunktion J0(x) auf ca. 14-15 Stellen *)
(* Computes the ordinary bessel function of the first kind of *)
(* order zero with argument x *)
(*----------------------------------------------------------------*)
PROCEDURE BesselJ1(x : LONGREAL) : LONGREAL;
(*---------------------------------------------------------------*)
(* Computes the ordinary bessel function of the first kind of *)
(* order one with argument x *)
(*---------------------------------------------------------------*)
PROCEDURE BesselJn(x : LONGREAL;
n : CARDINAL) : LONGREAL;
(*----------------------------------------------------------------*)
(* Berechnet die Besselsche Funktion erster Art N-ter Ordnung. *)
(*----------------------------------------------------------------*)
PROCEDURE BesselJN( x : LONGREAL;
n : INTEGER;
VAR Jn : ARRAY OF LONGREAL);
(*----------------------------------------------------------------*)
(* Generates an array of ordinary bessel functions of the first *)
(* kind of order l (l = 0,...,n) with argument x. *)
(* *)
(* x : the argument of the bessel functions *)
(* n : the upper bound of the indices of array j, n >= 0 *)
(* Jn : array j[0:n], on exit j[l] is the ordinary bessel *)
(* function of the first kind of order l and argument x. *)
(* *)
(* [3] Dautschi, W., "Computational aspects of three term *)
(* recurrence relations", SIAM review, 9, pp 24-82 (1967) *)
(*----------------------------------------------------------------*)
PROCEDURE ZeroBesselJ0 (n : INTEGER) : LONGREAL;
(*----------------------------------------------------------------*)
(* Compute the n-th zero of the Bessel function of order 0 *)
(* (BesselJ0) (the 0-th zero being 0), input parameter n beeing *)
(* the order of the desired zero with n > 0 *)
(* *)
(* Derived from Pascal mathlib library *)
(*----------------------------------------------------------------*)
PROCEDURE ZeroBesselJ1(n : CARDINAL) : LONGREAL;
(*----------------------------------------------------------------*)
(* Compute the n-th zero of the Bessel function of order 1 *)
(* (BesselJ1) (the 0-th zero being 0), input parameter n beeing *)
(* the order of the desired zero *)
(* *)
(* Derived from Pascal mathlib library *)
(*----------------------------------------------------------------*)
PROCEDURE BesselY0(x : LONGREAL) : LONGREAL;
(*----------------------------------------------------------------*)
(* Berechnet die Besselsche Funktion zweiter Art 0-ter Ordnung. *)
(*----------------------------------------------------------------*)
PROCEDURE DBesselY1(X : LONGREAL) : LONGREAL;
(*----------------------------------------------------------------*)
(* Berechnet die Bessel Function zweiter Art der Ordnung eins *)
(* des Arguments X. Abgeleitet aus der CERN library 2006. *)
(*----------------------------------------------------------------*)
PROCEDURE BesselY01( x : LONGREAL;
VAR y0,y1 : LONGREAL);
(*---------------------------------------------------------------*)
(* Computes the ordinary bessel functions of the second kind of *)
(* orders zero and one with argument x, x > 0 *)
(* *)
(* x : the argument of the bessel functions, x > 0 *)
(* y0 : on exit y0 has the value of the ordinary bessel function *)
(* of the second kind of order 0 and argument x *)
(* y1 : on exit y1 has the value of the ordinary bessel function *)
(* of the second kind of order 1 and argument x *)
(*---------------------------------------------------------------*)
PROCEDURE Hankel01(x : LONGREAL) : LONGCOMPLEX;
(*----------------------------------------------------------------*)
(* Berechnet die komplexe Hankel-Funktion erster Art der *)
(* Ordnung 0 f"ur das Argument x. ACM Algorithmus 124 fuer x < 8, *)
(* asymtotische Entwicklung fuer x > 17.5, J0,Y0 sonst *)
(* *)
(* [1] Schaefer, Luis J.; Comm. of the ACM 5(9), 483 (1962) *)
(* [2] Abramowitz, M.; Stegun, I.; Handbook of Mathematical *)
(* Functions with Formulas, Graphs, and Mathematical Tables, *)
(* Washington, D. C.: U.S. Government Printing Office, 1972. *)
(*----------------------------------------------------------------*)
END SpezFunkt3.