/*
 * bernpoly - Bernoully polynomials B_n(z) for arbitrary n,z..
 *
 * Copyright (C) 2013 Christoph Zurnieden
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * @(#) $Revision: 30.4 $
 * @(#) $Id: bernpoly.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
 * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/bernpoly.cal,v $
 *
 * Under source code control:	2013/08/11 01:31:28
 * File existed as early as:	2013
 */


static resource_debug_level;
resource_debug_level = config("resource_debug", 0);


read -once zeta2


/* Idea by Don Zagier */
define bernpoly(n,z){
  local h s c k;
  if(isint(n) && n>=0){
    h=0;s=0;c=-1;
    for(k=1;k<=n+1;k++){
      c*=1-(n+2)/k;
      s+=z^n;
      z++;
      h+=c*s/k;
    }
    return h;
  }
  else return -n*hurwitzzeta(1-n,z);
}


/*
 * restore internal function from resource debugging
 */
config("resource_debug", resource_debug_level),;
if (config("resource_debug") & 3) {
    print "bernpoly(n,z)";
}