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